Smallest multiple

Task

Task desciption is taken from Project Euler
(https://projecteuler.net/problem=5)
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Go

Translation of: Wren

Library: Go-rcu

<lang go>package main

import (

   "fmt"
   "math/big"
   "rcu"

)

func lcm(n int) *big.Int {

   lcm := big.NewInt(1)
   t := new(big.Int)
   for _, p := range rcu.Primes(n) {
       f := p
       for f*p <= n {
           f *= p
       }
       lcm.Mul(lcm, t.SetUint64(uint64(f)))
   }
   return lcm

}

func main() {

   fmt.Println("The LCMs of the numbers 1 to N inclusive is:")
   for _, i := range []int{10, 20, 200, 2000} {
       fmt.Printf("%4d: %s\n", i, lcm(i))
   }

}</lang>

Output:

The LCMs of the numbers 1 to N inclusive is:
  10: 2520
  20: 232792560
 200: 337293588832926264639465766794841407432394382785157234228847021917234018060677390066992000
2000: 151117794877444315307536308337572822173736308853579339903227904473000476322347234655122160866668946941993951014270933512030194957221371956828843521568082173786251242333157830450435623211664308500316844478617809101158220672108895053508829266120497031742749376045929890296052805527212315382805219353316270742572401962035464878235703759464796806075131056520079836955770415021318508272982103736658633390411347759000563271226062182345964184167346918225243856348794013355418404695826256911622054015423611375261945905974225257659010379414787547681984112941581325198396634685659217861208771400322507388161967513719166366839894214040787733471287845629833993885413462225294548785581641804620417256563685280586511301918399010451347815776570842790738545306707750937624267501103840324470083425714138183905657667736579430274197734179172691637931540695631396056193786415805463680000

Pascal

Here the simplest way, like Raku, check the highest exponent of every prime in range
Using harded coded primes. <lang pascal>{$IFDEF FPC}

 {$MODE DELPHI}

{$ELSE}

 {$APPTAYPE CONSOLE}

{$ENDIF} const

smallprimes : array[0..10] of Uint32 = (2,3,5,7,11,13,17,19,23,29,31);
MAX = 20;

function getmaxfac(pr: Uint32): Uint32; //get the pr^highest exponent of prime used in 2 .. MAX var

 i,fac : integer;

Begin

 result := pr;
 while pr*result <= MAX do
   result *= pr;

end;

var

 n,pr,prIdx : Uint32;

BEGIN

 n := 1;
 prIdx := 0;
 pr := smallprimes[prIdx];
 repeat
   pr := smallprimes[prIdx];
   n *= getmaxfac(pr);
   inc(prIdx);
   pr := smallprimes[prIdx];
 until pr>MAX;
 writeln(n);

{$IFDEF WINDOWS}

 READLN;

{$ENDIF} END. </lang>

Output:

232792560

Raku

Exercise with some larger values as well.

<lang perl6>use Prime::Factor;

sub minimum-multiple ($n where * > 1) {

   my %max-factor;
   for 2..$n { .&prime-factors.Bag.map: { %max-factor{.key} max= .value } }
   [*] flat %max-factor.map: { .key xx .value }

}

say "$_: ", .&minimum-multiple for <10 20 200 2000>; printf "%.3f seconds elapsed\n", now - INIT now;</lang>

Output:

10: 2520
20: 232792560
200: 337293588832926264639465766794841407432394382785157234228847021917234018060677390066992000
2000: 151117794877444315307536308337572822173736308853579339903227904473000476322347234655122160866668946941993951014270933512030194957221371956828843521568082173786251242333157830450435623211664308500316844478617809101158220672108895053508829266120497031742749376045929890296052805527212315382805219353316270742572401962035464878235703759464796806075131056520079836955770415021318508272982103736658633390411347759000563271226062182345964184167346918225243856348794013355418404695826256911622054015423611375261945905974225257659010379414787547681984112941581325198396634685659217861208771400322507388161967513719166366839894214040787733471287845629833993885413462225294548785581641804620417256563685280586511301918399010451347815776570842790738545306707750937624267501103840324470083425714138183905657667736579430274197734179172691637931540695631396056193786415805463680000
0.315 seconds elapsed

Ring

<lang ring> see "working..." + nl see "Smallest multiple is:" + nl n = 0

while true

     n++
     flag = 0
     for m = 1 to 20
         if n % m = 0
            flag += 1
         ok
     next
     if flag = 20
        see "" + n + nl
        exit
     ok

end

see "done..." + nl </lang>

Output:

working...
Smallest multiple is:
232792560
done...

Wren

Library: Wren-math

Library: Wren-big

Library: Wren-fmt

We don't really need a computer for the task as set because it's just the product of the maximum prime powers <= 20 which is : 16 x 9 x 5 x 7 x 11 x 13 x 17 x 19 = 232,792,560.

More formally and quite quick by Wren standards at 0.017 seconds: <lang ecmascript>import "./math" for Int import "./big" for BigInt import "./fmt" for Fmt

var lcm = Fn.new { |n|

   var primes = Int.primeSieve(n)
   var lcm = BigInt.one
   for (p in primes) {
       var f = p
       while (f * p <= n) f = f * p
       lcm = lcm * f
   }
   return lcm

}

System.print("The LCMs of the numbers 1 to N inclusive is:") for (i in [10, 20, 200, 2000]) Fmt.print("$,5d: $,i", i, lcm.call(i))</lang>

Output:

The LCMs of the numbers 1 to N inclusive is:
   10: 2,520
   20: 232,792,560
  200: 337,293,588,832,926,264,639,465,766,794,841,407,432,394,382,785,157,234,228,847,021,917,234,018,060,677,390,066,992,000
2,000: 151,117,794,877,444,315,307,536,308,337,572,822,173,736,308,853,579,339,903,227,904,473,000,476,322,347,234,655,122,160,866,668,946,941,993,951,014,270,933,512,030,194,957,221,371,956,828,843,521,568,082,173,786,251,242,333,157,830,450,435,623,211,664,308,500,316,844,478,617,809,101,158,220,672,108,895,053,508,829,266,120,497,031,742,749,376,045,929,890,296,052,805,527,212,315,382,805,219,353,316,270,742,572,401,962,035,464,878,235,703,759,464,796,806,075,131,056,520,079,836,955,770,415,021,318,508,272,982,103,736,658,633,390,411,347,759,000,563,271,226,062,182,345,964,184,167,346,918,225,243,856,348,794,013,355,418,404,695,826,256,911,622,054,015,423,611,375,261,945,905,974,225,257,659,010,379,414,787,547,681,984,112,941,581,325,198,396,634,685,659,217,861,208,771,400,322,507,388,161,967,513,719,166,366,839,894,214,040,787,733,471,287,845,629,833,993,885,413,462,225,294,548,785,581,641,804,620,417,256,563,685,280,586,511,301,918,399,010,451,347,815,776,570,842,790,738,545,306,707,750,937,624,267,501,103,840,324,470,083,425,714,138,183,905,657,667,736,579,430,274,197,734,179,172,691,637,931,540,695,631,396,056,193,786,415,805,463,680,000