# Least common multiple

Least common multiple
You are encouraged to solve this task according to the task description, using any language you may know.

Compute the least common multiple of two integers.

Given   m   and   n,   the least common multiple is the smallest positive integer that has both   m   and   n   as factors.

Example

The least common multiple of 12 and 18 is 36, because 12 is a factor (12 × 3 = 36), and 18 is a factor (18 × 2 = 36), and there is no positive integer less than 36 that has both factors.   As a special case, if either   m   or   n   is zero, then the least common multiple is zero.

One way to calculate the least common multiple is to iterate all the multiples of   m,   until you find one that is also a multiple of   n.

If you already have   gcd   for greatest common divisor,   then this formula calculates   lcm.

${\displaystyle \operatorname {lcm} (m,n)={\frac {|m\times n|}{\operatorname {gcd} (m,n)}}}$

One can also find   lcm   by merging the prime decompositions of both   m   and   n.

## 8th

 : gcd \ a b -- gcd	dup 0 n:= if drop ;; then	tuck \ b a b	n:mod \ b a-mod-b	recurse ; 	 : lcm \ m n 	2dup \ m n m n	n:* \ m n m*n	n:abs \ m n abs(m*n)	-rot \ abs(m*n) m n 	gcd \ abs(m*n) gcd(m.n)	n:/mod \ abs / gcd 	nip \ abs div gcd; : demo \ n m -- 	2dup "LCM of " . . " and " . . " = " . lcm . ;	 12 18 demo cr-6 14 demo cr35  0 demo cr  bye
Output:
LCM of 18 and 12 = 36
LCM of 14 and -6 = 42
LCM of 0 and 35 = 0


with Ada.Text_IO; use Ada.Text_IO; procedure Lcm_Test is   function Gcd (A, B : Integer) return Integer is      M : Integer := A;      N : Integer := B;      T : Integer;   begin      while N /= 0 loop         T := M;         M := N;         N := T mod N;      end loop;      return M;   end Gcd;    function Lcm (A, B : Integer) return Integer is   begin      if A = 0 or B = 0 then         return 0;      end if;      return abs (A) * (abs (B) / Gcd (A, B));   end Lcm;begin   Put_Line ("LCM of 12, 18 is" & Integer'Image (Lcm (12, 18)));   Put_Line ("LCM of -6, 14 is" & Integer'Image (Lcm (-6, 14)));   Put_Line ("LCM of 35, 0 is" & Integer'Image (Lcm (35, 0)));end Lcm_Test;

Output:

LCM of 12, 18 is 36
LCM of -6, 14 is 42
LCM of 35, 0 is 0

## ALGOL 68

 BEGIN   PROC gcd = (INT m, n) INT :   BEGIN      INT a := ABS m, b := ABS n;      IF a=0 OR b=0 THEN 0 ELSE	 WHILE b /= 0 DO INT t = b; b := a MOD b; a := t OD;	 a      FI   END;   PROC lcm = (INT m, n) INT : ( m*n = 0 | 0 | ABS (m*n) % gcd (m, n));   INT m=12, n=18;   printf (($gxg(0)3(xgxg(0))l$,	    "The least common multiple of", m, "and", n, "is", lcm(m,n),	    "and their greatest common divisor is", gcd(m,n)))END
Output:
The least common multiple of 12 and 18 is 36 and their greatest common divisor is 6



Note that either or both PROCs could just as easily be implemented as OPs but then the operator priorities would also have to be declared.

## ALGOL W

begin    integer procedure gcd ( integer value a, b ) ;        if b = 0 then a else gcd( b, a rem abs(b) );     integer procedure lcm( integer value a, b ) ;        abs( a * b ) div gcd( a, b );     write( lcm( 15, 20  ) );end.

## APL

APL provides this function.

      12^1836

If for any reason we wanted to reimplement it, we could do so in terms of the greatest common divisor by transcribing the formula set out in the task specification into APL notation:

      LCM←{(|⍺×⍵)÷⍺∨⍵}      12 LCM 1836

## AppleScript

-- LEAST COMMON MULTIPLE ----------------------------------------------------- -- lcm :: Integral a => a -> a -> aon lcm(x, y)    if x = 0 or y = 0 then        0    else        abs(x div (gcd(x, y)) * y)    end ifend lcm  -- TEST ----------------------------------------------------------------------on run     lcm(12, 18)     --> 36end run -- GENERIC FUNCTIONS --------------------------------------------------------- -- abs :: Num a => a -> aon abs(x)    if x < 0 then        -x    else        x    end ifend abs -- gcd :: Integral a => a -> a -> aon gcd(x, y)    script        on |λ|(a, b)            if b = 0 then                a            else                |λ|(b, a mod b)            end if        end |λ|    end script     result's |λ|(abs(x), abs(y))end gcd
Output:
36

## Arendelle

For GCD function check out here

< a , b >

( return ,

abs ( @a * @b ) /
!gcd( @a , @b )

)

## Assembly

### x86 Assembly

 ; lcm.asm: calculates the least common multiple; of two positive integers;; nasm x86_64 assembly (linux) with libc; assemble: nasm -felf64 lcm.asm; gcc lcm.o; usage: ./a.out [number1] [number2]     global main    extern printf ; c function: prints formatted output    extern strtol ; c function: converts strings to longs     section .text main:    push rbp    ; set up stack frame     ; rdi contains argc    ; if less than 3, exit    cmp rdi, 3    jl incorrect_usage     ; push first argument as number    push rsi    mov rdi, [rsi+8]    mov rsi, 0    mov rdx, 10 ; base 10    call strtol    pop rsi    push rax     ; push second argument as number    push rsi    mov rdi, [rsi+16]    mov rsi, 0    mov rdx, 10 ; base 10    call strtol    pop rsi    push rax     ; pop arguments and call get_gcd    pop rdi    pop rsi    call get_gcd     ; print value    mov rdi, print_number    mov rsi, rax    call printf     ; exit    mov rax, 0  ; 0--exit success    pop rbp    ret incorrect_usage:    mov rdi, bad_use_string    ; rsi already contains argv    mov rsi, [rsi]    call printf    mov rax, 0  ; 0--exit success    pop rbp    ret bad_use_string:    db "Usage: %s [number1] [number2]",10,0 print_number:    db "%d",10,0 get_gcd:    push rbp    ; set up stack frame    mov rax, 0    jmp loop loop:    ; keep adding the first argument    ; to itself until a multiple    ; is found. then, return    add rax, rdi    push rax    mov rdx, 0    div rsi    cmp rdx, 0    pop rax    je gcd_found    jmp loop gcd_found:    pop rbp         ret

## AutoHotkey

LCM(Number1,Number2){ If (Number1 = 0 || Number2 = 0)  Return Var := Number1 * Number2 While, Number2  Num := Number2, Number2 := Mod(Number1,Number2), Number1 := Num Return, Var // Number1} Num1 = 12Num2 = 18MsgBox % LCM(Num1,Num2)

12 18
36
-6 14
42
35 0
0


## BASIC

### Applesoft BASIC

ported from BBC BASIC

10 DEF FN MOD(A) = INT((A / B - INT(A / B)) * B + .05) * SGN(A / B)20 INPUT"M=";M%30 INPUT"N=";N%40 GOSUB 10050 PRINT R60 END 100 REM LEAST COMMON MULTIPLE M% N%110 R = 0120 IF M% = 0 OR N% = 0 THEN RETURN130 A% = M% : B% = N% : GOSUB 200"GCD140 R = ABS(M%*N%)/R150 RETURN 200 REM GCD ITERATIVE EUCLID A% B%210 FOR B = B% TO 0 STEP 0220     C% = A%230     A% = B240     B = FN MOD(C%)250 NEXT B260 R = ABS(A%)270 RETURN

### BBC BASIC

       DEF FN_LCM(M%,N%)      IF M%=0 OR N%=0 THEN =0 ELSE =ABS(M%*N%)/FN_GCD_Iterative_Euclid(M%, N%)       DEF FN_GCD_Iterative_Euclid(A%, B%)      LOCAL C%      WHILE B%        C% = A%        A% = B%        B% = C% MOD B%      ENDWHILE      = ABS(A%)

## Batch File

@echo offsetlocal enabledelayedexpansionset num1=12set num2=18 call :lcm %num1% %num2%exit /b :lcm <input1> <input2>if %2 equ 0 (	set /a lcm = %num1%*%num2%/%1	echo LCM = !lcm!	pause>nul	goto :EOF)set /a res = %1 %% %2call :lcm %2 %res%goto :EOF
Output:
LCM = 36

## bc

Translation of: AWK
/* greatest common divisor */define g(m, n) {	auto t 	/* Euclid's method */	while (n != 0) {		t = m		m = n		n = t % n	}	return (m)} /* least common multiple */define l(m, n) {	auto r 	if (m == 0 || n == 0) return (0)	r = m * n / g(m, n)	if (r < 0) return (-r)	return (r)}

## EchoLisp

(lcm a b) is already here as a two arguments function. Use foldl to find the lcm of a list of numbers.

 (lcm 0 9) → 0(lcm 444 888)→ 888(lcm 888 999) → 7992 (define (lcm* list) (foldl lcm (first list) list)) → lcm*(lcm* '(444 888 999)) → 7992

## Elena

Translation of: C#

ELENA 3.2 :

import extensions.import system'math. gcd = (:m:n)((n == 0)iif(m absolute, $(gcd eval(n,n mod:m)))). lcm = (:m:n)((m * n) absolute / gcd eval(m,n)). program =[ console printLine("lcm(12,18)=",lcm eval(12,18)).]. Output: lcm(12,18)=36  ## Elixir defmodule RC do def gcd(a,0), do: abs(a) def gcd(a,b), do: gcd(b, rem(a,b)) def lcm(a,b), do: div(abs(a*b), gcd(a,b))end IO.puts RC.lcm(-12,15) Output: 60  ## Erlang % Implemented by Arjun Sunel-module(lcm).-export([main/0]). main() -> lcm(-3,4). gcd(A, 0) -> A; gcd(A, B) -> gcd(B, A rem B). lcm(A,B) -> abs(A*B div gcd(A,B)). Output: 12  ## ERRE PROGRAM LCM PROCEDURE GCD(A,B->GCD) LOCAL C WHILE B DO C=A A=B B=C MOD B END WHILE GCD=ABS(A)END PROCEDURE PROCEDURE LCM(M,N->LCM) IF M=0 OR N=0 THEN LCM=0 EXIT PROCEDURE ELSE GCD(M,N->GCD) LCM=ABS(M*N)/GCD END IFEND PROCEDURE BEGIN LCM(18,12->LCM) PRINT("LCM of 18 AND 12 =";LCM) LCM(14,-6->LCM) PRINT("LCM of 14 AND -6 =";LCM) LCM(0,35->LCM) PRINT("LCM of 0 AND 35 =";LCM)END PROGRAM Output: LCM of 18 and 12 = 36 LCM of 14 and -6 = 42 LCM of 0 and 35 = 0  ## Euphoria function gcd(integer m, integer n) integer tmp while m do tmp = m m = remainder(n,m) n = tmp end while return nend function function lcm(integer m, integer n) return m / gcd(m, n) * nend function ## Excel Excel's LCM can handle multiple values. Type in a cell: =LCM(A1:J1) This will get the LCM on the first 10 cells in the first row. Thus : 12 3 5 23 13 67 15 9 4 2 3605940 ## Ezhil  ## இந்த நிரல் இரு எண்களுக்கு இடையிலான மீச்சிறு பொது மடங்கு (LCM), மீப்பெரு பொது வகுத்தி (GCD) என்ன என்று கணக்கிடும் நிரல்பாகம் மீபொம(எண்1, எண்2) @(எண்1 == எண்2) ஆனால் ## இரு எண்களும் சமம் என்பதால், மீபொம அந்த எண்ணேதான் பின்கொடு எண்1 @(எண்1 > எண்2) இல்லைஆனால் சிறியது = எண்2 பெரியது = எண்1 இல்லை சிறியது = எண்1 பெரியது = எண்2 முடி மீதம் = பெரியது % சிறியது @(மீதம் == 0) ஆனால் ## பெரிய எண்ணில் சிறிய எண் மீதமின்றி வகுபடுவதால், பெரிய எண்தான் மீபொம பின்கொடு பெரியது இல்லை தொடக்கம் = பெரியது + 1 நிறைவு = சிறியது * பெரியது @(எண் = தொடக்கம், எண் <= நிறைவு, எண் = எண் + 1) ஆக ## ஒவ்வோர் எண்ணாக எடுத்துக்கொண்டு தரப்பட்ட இரு எண்களாலும் வகுத்துப் பார்க்கின்றோம். முதலாவதாக இரண்டாலும் மீதமின்றி வகுபடும் எண்தான் மீபொம மீதம்1 = எண் % சிறியது மீதம்2 = எண் % பெரியது @((மீதம்1 == 0) && (மீதம்2 == 0)) ஆனால் பின்கொடு எண் முடி முடி முடி முடி அ = int(உள்ளீடு("ஓர் எண்ணைத் தாருங்கள் "))ஆ = int(உள்ளீடு("இன்னோர் எண்ணைத் தாருங்கள் ")) பதிப்பி "நீங்கள் தந்த இரு எண்களின் மீபொம (மீச்சிறு பொது மடங்கு, LCM) = ", மீபொம(அ, ஆ)  ## F# let rec gcd x y = if y = 0 then abs x else gcd y (x % y) let lcm x y = x * y / (gcd x y) ## Factor The vocabulary math.functions already provides lcm. USING: math.functions prettyprint ;26 28 lcm . This program outputs 364. One can also reimplement lcm. USING: kernel math prettyprint ;IN: script : gcd ( a b -- c ) [ abs ] [ [ nip ] [ mod ] 2bi gcd ] if-zero ; : lcm ( a b -- c ) [ * abs ] [ gcd ] 2bi / ; 26 28 lcm . ## Forth : gcd ( a b -- n ) begin dup while tuck mod repeat drop ; : lcm ( a b -- n ) over 0= over 0= or if 2drop 0 exit then 2dup gcd abs */ ; ## Fortran This solution is written as a combination of 2 functions, but a subroutine implementation would work great as well.  integer function lcm(a,b) integer:: a,b lcm = a*b / gcd(a,b) end function lcm integer function gcd(a,b) integer :: a,b,t do while (b/=0) t = b b = mod(a,b) a = t end do gcd = abs(a) end function gcd  ## FreeBASIC ' FB 1.05.0 Win64 Function lcm (m As Integer, n As Integer) As Integer If m = 0 OrElse n = 0 Then Return 0 If m < n Then Swap m, n '' to minimize iterations needed Var count = 0 Do count +=1 Loop Until (m * count) Mod n = 0 Return m * countEnd Function Print "lcm(12, 18) ="; lcm(12, 18)Print "lcm(15, 12) ="; lcm(15, 12)Print "lcm(10, 14) ="; lcm(10, 14)PrintPrint "Press any key to quit"Sleep Output: lcm(12, 18) = 36 lcm(15, 12) = 60 lcm(10, 14) = 70  ## Frink Frink has a built-in LCM function that handles arbitrarily-large integers.  println[lcm[2562047788015215500854906332309589561, 6795454494268282920431565661684282819]]  ## FunL FunL has function lcm in module integers with the following definition: def lcm( _, 0 ) = 0 lcm( 0, _ ) = 0 lcm( x, y ) = abs( (x\gcd(x, y)) y ) ## GAP # Built-inLcmInt(12, 18);# 36 ## Go package main import ( "fmt" "math/big") var m, n, z big.Int func init() { m.SetString("2562047788015215500854906332309589561", 10) n.SetString("6795454494268282920431565661684282819", 10)} func main() { fmt.Println(z.Mul(z.Div(&m, z.GCD(nil, nil, &m, &n)), &n))} Output: 15669251240038298262232125175172002594731206081193527869  ## Groovy def gcdgcd = { m, n -> m = m.abs(); n = n.abs(); n == 0 ? m : m%n == 0 ? n : gcd(n, m % n) } def lcd = { m, n -> Math.abs(m * n) / gcd(m, n) } [[m: 12, n: 18, l: 36], [m: -6, n: 14, l: 42], [m: 35, n: 0, l: 0]].each { t -> println "LCD of$t.m, $t.n is$t.l"    assert lcd(t.m, t.n) == t.l}
Output:
LCD of 12, 18 is 36
LCD of -6, 14 is 42
LCD of 35, 0 is 0

That is already available as the function lcm in the Prelude. Here's the implementation:

lcm :: (Integral a) => a -> a -> alcm _ 0 =  0lcm 0 _ =  0lcm x y =  abs ((x quot (gcd x y)) * y)

## Icon and Unicon

The lcm routine from the Icon Programming Library uses gcd. The routine is

link numbers procedure main()write("lcm of 18, 36 = ",lcm(18,36))write("lcm of 0, 9 36 = ",lcm(0,9))end

numbers provides lcm and gcd and looks like this:

procedure lcm(i, j)		#: least common multiple   if (i =  0) | (j = 0) then return 0	   return abs(i * j) / gcd(i, j)end

## J

J provides the dyadic verb *. which returns the least common multiple of its left and right arguments.

      12 *. 1836   12 *. 18 2236 132   *./ 12 18 22396   0 1 0 1 *. 0 0 1 1  NB. for truth valued arguments (0 and 1) it is equivalent to "and"0 0 0 1   *./~ 0 10 00 1

Note: least common multiple is the original boolean multiplication. Constraining the universe of values to 0 and 1 allows us to additionally define logical negation (and boolean algebra was redefined to include this constraint in the early 1900s - the original concept of boolean algebra is now known as a boolean ring).

## Java

import java.util.Scanner; public class LCM{   public static void main(String[] args){      Scanner aScanner = new Scanner(System.in);       //prompts user for values to find the LCM for, then saves them to m and n      System.out.print("Enter the value of m:");      int m = aScanner.nextInt();      System.out.print("Enter the value of n:");      int n = aScanner.nextInt();      int lcm = (n == m || n == 1) ? m :(m == 1 ? n : 0);      /* this section increases the value of mm until it is greater        / than or equal to nn, then does it again when the lesser       / becomes the greater--if they aren't equal. If either value is 1,      / no need to calculate*/      if (lcm == 0) {         int mm = m, nn = n;         while (mm != nn) {             while (mm < nn) { mm += m; }             while (nn < mm) { nn += n; }         }           lcm = mm;      }      System.out.println("lcm(" + m + ", " + n + ") = " + lcm);   }}

## JavaScript

### ES5

Computing the least common multiple of an integer array, using the associative law:

${\displaystyle \operatorname {lcm} (a,b,c)=\operatorname {lcm} (\operatorname {lcm} (a,b),c),}$

${\displaystyle \operatorname {lcm} (a_{1},a_{2},\ldots ,a_{n})=\operatorname {lcm} (\operatorname {lcm} (a_{1},a_{2},\ldots ,a_{n-1}),a_{n}).}$

function LCM(A)  // A is an integer array (e.g. [-50,25,-45,-18,90,447]){       var n = A.length, a = Math.abs(A[0]);    for (var i = 1; i < n; i++)     { var b = Math.abs(A[i]), c = a;       while (a && b){ a > b ? a %= b : b %= a; }        a = Math.abs(c*A[i])/(a+b);     }    return a;} /* For example:   LCM([-50,25,-45,-18,90,447]) -> 67050*/

### ES6

(() => {    'use strict';     // gcd :: Integral a => a -> a -> a    let gcd = (x, y) => {        let _gcd = (a, b) => (b === 0 ? a : _gcd(b, a % b)),            abs = Math.abs;        return _gcd(abs(x), abs(y));    }     // lcm :: Integral a => a -> a -> a    let lcm = (x, y) =>        x === 0 || y === 0 ? 0 : Math.abs(Math.floor(x / gcd(x, y)) * y);     // TEST    return lcm(12, 18); })();
Output:
36

## jq

Direct method

# Define the helper function to take advantage of jq's tail-recursion optimizationdef lcm(m; n):  def _lcm:    # state is [m, n, i]    if (.[2] % .[1]) == 0 then .[2] else (.[0:2] + [.[2] + m]) | _lcm end;  [m, n, m] | _lcm;

## Julia

Built-in function:

lcm(m,n)

## K

   gcd:{:[~x;y;_f[y;x!y]]}   lcm:{_abs _ x*y%gcd[x;y]}    lcm .'(12 18; -6 14; 35 0)36 42 0    lcm/1+!20232792560

## Kotlin

fun main(args: Array<String>) {    fun gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)    fun lcm(a: Int, b: Int) = a * b / gcd(a, b)    println(lcm(15, 9))}

## LabVIEW

Requires GCD. This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code.

## Lasso

define gcd(a,b) => {	while(#b != 0) => {		local(t = #b)		#b = #a % #b		#a = #t	}	return #a}define lcm(m,n) => {	 #m == 0 || #n == 0 ? return 0	 local(r = (#m * #n) / decimal(gcd(#m, #n)))	 return integer(#r)->abs} lcm(-6, 14)lcm(2, 0)lcm(12, 18)lcm(12, 22)lcm(7, 31)
Output:
42
0
36
132
217

## Liberty BASIC

print "Least Common Multiple of 12 and 18 is ";LCM(12,18)end function LCM(m,n)    LCM=abs(m*n)/GCD(m,n)    end function function GCD(a,b)    while b        c = a        a = b        b = c mod b    wend    GCD = abs(a)    end function

## Logo

to abs :n  output sqrt product :n :nend to gcd :m :n  output ifelse :n = 0 [ :m ] [ gcd :n modulo :m :n ]end to lcm :m :n  output quotient (abs product :m :n) gcd :m :nend

Demo code:

print lcm 38 46

Output:

874

## Lua

function gcd( m, n )    while n ~= 0 do        local q = m        m = n        n = q % n    end    return mend function lcm( m, n )    return ( m ~= 0 and n ~= 0 ) and m * n / gcd( m, n ) or 0end print( lcm(12,18) )

## Maple

The least common multiple of two integers is computed by the built-in procedure ilcm in Maple. This should not be confused with lcm, which computes the least common multiple of polynomials.

> ilcm( 12, 18 );                                   36

## Mathematica

LCM[18,12]-> 36

## MATLAB / Octave

 lcm(a,b)

## Maxima

lcm(a, b);   /* a and b may be integers or polynomials */ /* In Maxima the gcd of two integers is always positive, and a * b = gcd(a, b) * lcm(a, b),so the lcm may be negative. To get a positive lcm, simply do */ abs(lcm(a, b))

## МК-61/52

ИПA	ИПB	*	|x|	ПC	ИПA	ИПB	/	[x]	П9ИПA	ИПB	ПA	ИП9	*	-	ПB	x=0	05	ИПCИПA	/	С/П

## ML

### mLite

fun gcd (a, 0) = a      | (0, b) = b      | (a, b) where (a < b)               = gcd (a, b rem a)      | (a, b) = gcd (b, a rem b) fun lcm (a, b) = let val d = gcd (a, b)                 in a * b div d                 end

## NetRexx

/* NetRexx */options replace format comments java crossref symbols nobinary numeric digits 3000 runSample(arg)return -- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~method lcm(m_, n_) public static  L_ = m_ * n_ % gcd(m_, n_)  return L_ -- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~-- Euclid's algorithm - iterative implementationmethod gcd(m_, n_) public static  loop while n_ > 0    c_ = m_ // n_    m_ = n_    n_ = c_    end  return m_ -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method runSample(arg) private static  parse arg samples  if samples = '' | samples = '.' then    samples = '-6 14 =    42 |' -               '3  4 =    12 |' -              '18 12 =    36 |' -               '2  0 =     0 |' -               '0 85 =     0 |' -              '12 18 =    36 |' -               '5 12 =    60 |' -              '12 22 =   132 |' -               '7 31 =   217 |' -             '117 18 =   234 |' -              '38 46 =   874 |' -           '18 12 -5 =   180 |' -           '-5 18 12 =   180 |' - -- confirm that other permutations work           '12 -5 18 =   180 |' -        '18 12 -5 97 = 17460 |' -              '30 42 =   210 |' -              '30 42 =     . |' - -- 210; no verification requested              '18 12'             -- 36   loop while samples \= ''    parse samples sample '|' samples    loop while sample \= ''      parse sample mnvals '=' chk sample      if chk = '' then chk = '.'      mv = mnvals.word(1)      loop w_ = 2 to mnvals.words mnvals        nv = mnvals.word(w_)        mv = mv.abs        nv = nv.abs        mv = lcm(mv, nv)        end w_      lv = mv      select case chk        when '.' then state = ''        when lv  then state = '(verified)'        otherwise     state = '(failed)'        end      mnvals = mnvals.space(1, ',').changestr(',', ', ')      say 'lcm of' mnvals.right(15.max(mnvals.length)) 'is' lv.right(5.max(lv.length)) state      end    end   return
Output:
lcm of          -6, 14 is    42 (verified)
lcm of            3, 4 is    12 (verified)
lcm of          18, 12 is    36 (verified)
lcm of            2, 0 is     0 (verified)
lcm of           0, 85 is     0 (verified)
lcm of          12, 18 is    36 (verified)
lcm of           5, 12 is    60 (verified)
lcm of          12, 22 is   132 (verified)
lcm of           7, 31 is   217 (verified)
lcm of         117, 18 is   234 (verified)
lcm of          38, 46 is   874 (verified)
lcm of      18, 12, -5 is   180 (verified)
lcm of      -5, 18, 12 is   180 (verified)
lcm of      12, -5, 18 is   180 (verified)
lcm of  18, 12, -5, 97 is 17460 (verified)
lcm of          30, 42 is   210 (verified)
lcm of          30, 42 is   210
lcm of          18, 12 is    36


## Nim

proc gcd(u, v): auto =  var    t = 0    u = u    v = v  while v != 0:    t = u    u = v    v = t %% v  abs(u) proc lcm(a, b): auto = abs(a * b) div gcd(a, b) echo lcm(12, 18)echo lcm(-6, 14)

## Objeck

Translation of: C
 class LCM {  function : Main(args : String[]) ~ Nil {    IO.Console->Print("lcm(35, 21) = ")->PrintLine(lcm(21,35));  }   function : lcm(m : Int, n : Int) ~ Int {    return m / gcd(m, n) * n;  }   function : gcd(m : Int, n : Int) ~ Int {    tmp : Int;    while(m <> 0) { tmp := m; m := n % m; n := tmp; };    return n;  }}

## OCaml

let rec gcd u v =  if v <> 0 then (gcd v (u mod v))  else (abs u) let lcm m n =  match m, n with  | 0, _ | _, 0 -> 0  | m, n -> abs (m * n) / (gcd m n) let () =  Printf.printf "lcm(35, 21) = %d\n" (lcm 21 35)

## Oforth

lcm is already defined into Integer class :

12 18 lcm

## ooRexx

 say lcm(18, 12) -- calculate the greatest common denominator of a numerator/denominator pair::routine gcd private  use arg x, y   loop while y \= 0      -- check if they divide evenly      temp = x // y      x = y      y = temp  end  return x -- calculate the least common multiple of a numerator/denominator pair::routine lcm private  use arg x, y  return x / gcd(x, y) * y

## Order

Translation of: bc
#include <order/interpreter.h> #define ORDER_PP_DEF_8gcd ORDER_PP_FN( \8fn(8U, 8V,                            \    8if(8isnt_0(8V), 8gcd(8V, 8remainder(8U, 8V)), 8U))) #define ORDER_PP_DEF_8lcm ORDER_PP_FN( \8fn(8X, 8Y,                            \    8if(8or(8is_0(8X), 8is_0(8Y)),     \        0,                             \        8quotient(8times(8X, 8Y), 8gcd(8X, 8Y)))))// No support for negative numbers ORDER_PP( 8to_lit(8lcm(12, 18)) )   // 36

## PARI/GP

Built-in function:

lcm

## Pascal

Program LeastCommonMultiple(output); function lcm(a, b: longint): longint;  begin    lcm := a;    while (lcm mod b) <> 0 do      inc(lcm, a);  end; begin  writeln('The least common multiple of 12 and 18 is: ', lcm(12, 18));end.

Output:

The least common multiple of 12 and 18 is: 36


## Perl

Using GCD:

sub gcd {	my ($a,$b) = @_;	while ($a) { ($a, $b) = ($b % $a,$a) }	$b} sub lcm { my ($a, $b) = @_; ($a && $b) and$a / gcd($a,$b) * $b or 0} print lcm(1001, 221); Or by repeatedly increasing the smaller of the two until LCM is reached: sub lcm { use integer; my ($x, $y) = @_; my ($a, $b) = @_; while ($a != $b) { ($a, $b,$x, $y) = ($b, $a,$y, $x) if$a > $b;$a = $b /$x * $x;$a += $x if$a < $b; }$a} print lcm(1001, 221);

## Perl 6

This function is provided as an infix so that it can be used productively with various metaoperators.

say 3 lcm 4;            # infixsay [lcm] 1..20;        # reductionsay ~(1..10 Xlcm 1..10) # cross
Output:
12
232792560
1 2 3 4 5 6 7 8 9 10 2 2 6 4 10 6 14 8 18 10 3 6 3 12 15 6 21 24 9 30 4 4 12 4 20 12 28 8 36 20 5 10 15 20 5 30 35 40 45 10 6 6 6 12 30 6 42 24 18 30 7 14 21 28 35 42 7 56 63 70 8 8 24 8 40 24 56 8 72 40 9 18 9 36 45 18 63 72 9 90 10 10 30 20 10 30 70 40 90 10

## Phix

function lcm(integer m, integer n)    return m / gcd(m, n) * nend function

## PHP

Translation of: D

### version 2

version2 is faster than version1

 function gcd ($a,$b)  {    function pgcd ($n,$m)  {        if($n -le$m) {             if($n -eq 0) {$m}            else{pgcd $n ($m%$n)} } else {pgcd$m $n} }$n = [Math]::Abs($a)$m = [Math]::Abs($b) (pgcd$n $m)}function lcm ($a, $b) { [Math]::Abs($a*$b)/(gcd$a $b)}lcm 12 18  Output: 36  ## Prolog SWI-Prolog knows gcd. lcm(X, Y, Z) :- Z is abs(X * Y) / gcd(X,Y). Example:  ?- lcm(18,12, Z). Z = 36.  ## PureBasic Procedure GCDiv(a, b); Euclidean algorithm Protected r While b r = b b = a%b a = r Wend ProcedureReturn aEndProcedure Procedure LCM(m,n) Protected t If m And n t=m*n/GCDiv(m,n) EndIf ProcedureReturn t*Sign(t)EndProcedure ## Python ### gcd Using the fractions libraries gcd function: >>> import fractions>>> def lcm(a,b): return abs(a * b) / fractions.gcd(a,b) if a and b else 0 >>> lcm(12, 18)36>>> lcm(-6, 14)42>>> assert lcm(0, 2) == lcm(2, 0) == 0>>>  ### Prime decomposition This imports Prime decomposition#Python from prime_decomposition import decomposetry: reduceexcept NameError: from functools import reduce def lcm(a, b): mul = int.__mul__ if a and b: da = list(decompose(abs(a))) db = list(decompose(abs(b))) merge= da for d in da: if d in db: db.remove(d) merge += db return reduce(mul, merge, 1) return 0 if __name__ == '__main__': print( lcm(12, 18) ) # 36 print( lcm(-6, 14) ) # 42 assert lcm(0, 2) == lcm(2, 0) == 0 ### Iteration over multiples >>> def lcm(*values): values = set([abs(int(v)) for v in values]) if values and 0 not in values: n = n0 = max(values) values.remove(n) while any( n % m for m in values ): n += n0 return n return 0 >>> lcm(-6, 14)42>>> lcm(2, 0)0>>> lcm(12, 18)36>>> lcm(12, 18, 22)396>>>  ### Repeated modulo Translation of: Tcl >>> def lcm(p,q): p, q = abs(p), abs(q) m = p * q if not m: return 0 while True: p %= q if not p: return m // q q %= p if not q: return m // p >>> lcm(-6, 14)42>>> lcm(12, 18)36>>> lcm(2, 0)0>>>  ## Qi  (define gcd A 0 -> A A B -> (gcd B (MOD A B))) (define lcm A B -> (/ (* A B) (gcd A B)))  ## R  "%gcd%" <- function(u, v) {ifelse(u %% v != 0, v %gcd% (u%%v), v)} "%lcm%" <- function(u, v) { abs(u*v)/(u %gcd% v)} print (50 %lcm% 75)  ## Racket Racket already has defined both lcm and gcd funtions: #lang racket(lcm 3 4 5 6) ;returns 60(lcm 8 108) ;returns 216(gcd 8 108) ;returns 4(gcd 108 216 432) ;returns 108 ## Retro This is from the math extensions library included with Retro. : gcd ( ab-n ) [ tuck mod dup ] while drop ;: lcm ( ab-n ) 2over gcd [ * ] dip / ; ## REXX ### version 1 The lcm subroutine can handle any number of integers and/or arguments. The integers (negative/zero/positive) can be (as per the numeric digits) up to ten thousand digits. Usage note: the integers can be expressed as a list and/or specified as individual arguments (or as mixed). /*REXX program finds the LCM (Least Common Multiple) of any number of integers. */numeric digits 10000 /*can handle 10k decimal digit numbers.*/say 'the LCM of 19 and 0 is ───► ' lcm(19 0 )say 'the LCM of 0 and 85 is ───► ' lcm( 0 85 )say 'the LCM of 14 and -6 is ───► ' lcm(14, -6 )say 'the LCM of 18 and 12 is ───► ' lcm(18 12 )say 'the LCM of 18 and 12 and -5 is ───► ' lcm(18 12, -5 )say 'the LCM of 18 and 12 and -5 and 97 is ───► ' lcm(18, 12, -5, 97)say 'the LCM of 2**19-1 and 2**521-1 is ───► ' lcm(2**19-1 2**521-1) /* [↑] 7th & 13th Mersenne primes.*/exit /*stick a fork in it, we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/lcm: procedure; parse arg$,_; $=$ _;           do i=3  to arg();  $=$ arg(i);  end  /*i*/     parse var $x$                                  /*obtain the first value in args. */     x=abs(x)                                         /*use the absolute value of  X.   */               do  while $\=='' /*process the remainder of args. */ parse var$ ! $; if !<0 then !=-! /*pick off the next arg (ABS val).*/ if !==0 then return 0 /*if zero, then LCM is also zero. */ d=x*! /*calculate part of the LCM here. */ do until !==0; parse value x//! ! with ! x end /*until*/ /* [↑] this is a short & fast GCD*/ x=d%x /*divide the pre─calculated value.*/ end /*while*/ /* [↑] process subsequent args. */ return x /*return with the LCM of the args.*/ output when using the (internal) supplied list: the LCM of 19 and 0 is ───► 0 the LCM of 0 and 85 is ───► 0 the LCM of 14 and -6 is ───► 42 the LCM of 18 and 12 is ───► 36 the LCM of 18 and 12 and -5 is ───► 180 the LCM of 18 and 12 and -5 and 97 is ───► 17460 the LCM of 2**19-1 and 2**521-1 is ───► 3599124170836896975638715824247986405702540425206233163175195063626010878994006898599180426323472024265381751210505324617708575722407440034562999570663839968526337  ### version 2 Translation of: REXX version 0 using different argument handling- Use as lcm(a,b,c,---) lcm2: procedurex=abs(arg(1))do k=2 to arg() While x<>0 y=abs(arg(k)) x=x*y/gcd2(x,y) endreturn x gcd2: procedurex=abs(arg(1))do j=2 to arg() y=abs(arg(j)) If y<>0 Then Do do until z==0 z=x//y x=y y=z end end endreturn x ## Ring  see lcm(24,36) func lcm m,n lcm = m*n / gcd(m,n) return lcm func gcd gcd, b while b c = gcd gcd = b b = c % b end return gcd  ## Ruby Ruby has an Integer#lcm method, which finds the least common multiple of two integers. irb(main):001:0> 12.lcm 18=> 36 I can also write my own lcm method. This one takes any number of arguments. def gcd(m, n) m, n = n, m % n until n.zero? m.absend def lcm(*args) args.inject(1) do |m, n| return 0 if n.zero? (m * n).abs / gcd(m, n) endend p lcm 12, 18, 22p lcm 15, 14, -6, 10, 21 Output: 396 210  ## Run BASIC print lcm(22,44) function lcm(m,n) while n t = m m = n n = t mod n wendlcm = mend function ## Rust This implementation uses a recursive implementation of Stein's algorithm to calculate the gcd. use std::cmp::{min, max};fn gcd_stein(a: usize, b: usize) -> usize { match ((a, b), (a & 1, b & 1)) { ((x, y), _) if x == y => y, ((0, x), _) | ((x, 0), _) => x, ((x, y), (0, 1)) | ((y, x), (1, 0)) => gcd(x >> 1, y), ((x, y), (0, 0)) => gcd(x >> 1, y >> 1) << 1, ((x, y), (1, 1)) => { let (x, y) = (min(x, y), max(x, y)); gcd((y - x) >> 1, x) } _ => unreachable!(), }}fn lcm(a: usize, b: usize) -> usize { a * b / gcd_stein(a,b)} ## Scala def gcd(a: Int, b: Int):Int=if (b==0) a.abs else gcd(b, a%b)def lcm(a: Int, b: Int)=(a*b).abs/gcd(a,b) lcm(12, 18) // 36lcm( 2, 0) // 0lcm(-6, 14) // 42 ## Scheme > (lcm 108 8)216 ## Seed7 $ include "seed7_05.s7i"; const func integer: gcd (in var integer: a, in var integer: b) is func  result    var integer: gcd is 0;  local    var integer: help is 0;  begin    while a <> 0 do      help := b rem a;      b := a;      a := help;    end while;    gcd := b;  end func; const func integer: lcm (in integer: a, in integer: b) is  return a div gcd(a, b) * b; const proc: main is func  begin    writeln("lcm(35, 21) = " <& lcm(21, 35));  end func;

Original source: [1]

## Sidef

Built-in:

say Math.lcm(1001, 221)

Using GCD:

func gcd(a, b) {    while (a) { (a, b) = (b % a, a) }    return b} func lcm(a, b) {    (a && b) ? (a / gcd(a, b) * b) : 0} say lcm(1001, 221)
Output:
17017


## Smalltalk

Smalltalk has a built-in lcm method on SmallInteger:

12 lcm: 18

## Sparkling

function factors(n) {	var f = {}; 	for var i = 2; n > 1; i++ {		while n % i == 0 {			n /= i;			f[i] = f[i] != nil ? f[i] + 1 : 1;		}	} 	return f;} function GCD(n, k) {	let f1 = factors(n);	let f2 = factors(k); 	let fs = map(f1, function(factor, multiplicity) {		let m = f2[factor];		return m == nil ? 0 : min(m, multiplicity);	}); 	let rfs = {};	foreach(fs, function(k, v) {		rfs[sizeof rfs] = pow(k, v);	}); 	return reduce(rfs, 1, function(x, y) { return x * y; });} function LCM(n, k) {	return n * k / GCD(n, k);}

## Swift

Using the Swift GCD function.

func lcm(a:Int, b:Int) -> Int {    return abs(a * b) / gcd_rec(a, b)}

## uBasic/4tH

Translation of: BBC BASIC
Print "LCM of 12 : 18 = "; FUNC(_LCM(12,18)) End  _GCD_Iterative_Euclid Param(2)  Local (1)  Do While [email protected]    [email protected] = [email protected]    [email protected] = [email protected]    [email protected] = [email protected] % [email protected]  LoopReturn (ABS([email protected]))  _LCM Param(2)If [email protected]*[email protected]  Return (ABS([email protected]*[email protected])/FUNC(_GCD_Iterative_Euclid([email protected],[email protected])))Else  Return (0)EndIf
Output:
LCM of 12 : 18 = 36

0 OK, 0:330

## UNIX Shell

${\displaystyle \operatorname {lcm} (m,n)=\left|{\frac {m\times n}{\operatorname {gcd} (m,n)}}\right|}$

Works with: Bourne Shell

## Ursa

import "math"out (lcm 12 18) endl console
Output:
36

## Vala

 int lcm(int a, int b){    /*Return least common multiple of two ints*/    // check for 0's                                                                if (a == 0 || b == 0)	return 0;     // Math.abs(x) only works for doubles, Math.absf(x) for floats                  if (a < 0)        a *= -1;    if (b < 0)	b *= -1;     int x = 1;    while (true){        if (a * x % b == 0)            return a*x;        x++;    }} void main(){    int	a = 12;    int	b = 18;     stdout.printf("lcm(%d, %d) = %d\n",	a, b, lcm(a, b));}

## VBScript

Function LCM(a,b)	LCM = POS((a * b)/GCD(a,b))End Function Function GCD(a,b)	Do		If a Mod b > 0 Then			c = a Mod b			a = b			b = c		Else			GCD = b			Exit Do		End If	LoopEnd Function Function POS(n)	If n < 0 Then		POS = n * -1	Else		POS = n	End IfEnd Function i = WScript.Arguments(0)j = WScript.Arguments(1) WScript.StdOut.Write "The LCM of " & i & " and " & j & " is " & LCM(i,j) & "."WScript.StdOut.WriteLine
Output:
C:\>cscript /nologo lcm.vbs 12 18
The LCM of 12 and 18 is 36.

C:\>cscript /nologo lcm.vbs 14 -6
The LCM of 14 and -6 is 42.

C:\>cscript /nologo lcm.vbs 0 35
The LCM of 0 and 35 is 0.

C:\>

## Wortel

Operator

@lcm a b

Number expression

!#~km a b

Function (using gcd)

&[a b] *b /a @gcd a b

## XPL0

include c:\cxpl\codes; func GCD(M,N);  \Return the greatest common divisor of M and Nint  M, N;int  T;[while N do     \Euclid's method    [T:= M;  M:= N;  N:= rem(T/N)];return M;]; func LCM(M,N);  \Return least common multipleint  M, N;return abs(M*N) / GCD(M,N); \Display the LCM of two integers entered on command lineIntOut(0, LCM(IntIn(8), IntIn(8)))

## zkl

fcn lcm(m,n){ (m*n).abs()/m.gcd(n) }  // gcd is a number method
Output:
zkl: lcm(12,18)
36
zkl: lcm(-6,14)
42
zkl: lcm(35,0)
0