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"CodeGolf" challenge: write the shortest practical Least Common Multiple function that:

  1. Does not use built in GCD, LCM or any related fuctions
  2. Accepts multiple arguments in any order, e.g. LCM[3, 20, 6]
  3. In the spirit of the original, obfuscated is better
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Mr.Wizard
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3 Answers3

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New code, Golfing Simon's method (now v10-syntax compatible):

lcm = Fold[#/#2/._~_~x_|_:># x&,1,{##}]&

This was my original code from a tongue-in-cheek answer on StackOverflow:

gcd = If[#2==0,#,#2~#0~Mod@##]&
lcm = Fold[##/gcd@##&,#,{##2}]&

As a one-liner:

lcm = Fold[If[#2==0,#,#2~#0~Mod@##]&@##^-1##&,#,{##}]&

Intentionally obfuscated:

lcm = If[{}!={##2},#0[If[#2==0,#,#2~#0~Mod@##]&[#,#2]^-1#*#2,##3],#]&

The fact that it throws errors yet works just fine is part of the game.

Mr.Wizard
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  • Outstanding! It never occurred to me that you could deal with Rationals and Integers in a single rule. Brilliant stuff. I had a look to see if I could replace Fold with some #0 trickery, but the code to terminate the recursion is just too big. If only Fold was a longer word :-) I think this might just be unbeatable. – Simon Woods Jul 14 '12 at 12:20
  • @Simon Thanks. :-) Using | on the LHS of a pattern is one of my favorite "tricks." I too experimented with using #0 in place of Fold: that is my "Intentionally obfuscated" line at the end of my answer. By the way, if you use my Fold modification you can knock a couple of characters off of this code. – Mr.Wizard Jul 14 '12 at 18:12
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    @Mr.Wizard While musing these fine examples, I figured I couldn't run the first line of your beautiful solution, as now we have associations and #x results in errors. The problem is solved by inserting a space between them. – Stitch Jan 23 '17 at 18:43
  • @Stitch Thanks; fixed now. – Mr.Wizard Jun 14 '17 at 23:55
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I am not sure how this compares in terms of length but it does not throw errors and isn't even obfuscated:

lcm[ls__] := 
 Fold[Denominator[Together[Unique[x]/#1 + Unique[x]/#2]] &, 
  First[{ls}], Rest[{ls}]

Just to check it works:

f = RandomInteger[{1, 100}, 200];

lcm @@ f == LCM @@ f

True
Mr.Wizard
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Andrzej Kozlowski
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  • Thanks for answering. To format your code, select it and click the curly-brackets button above the text box. – Mr.Wizard Jan 25 '12 at 21:57
  • Yes, I did just that but as you beat me to it it wouldn't let me save my edits ;-) Come to think of it, I am not even sure if using addition of fractions violates the condition about not using "related functions"... – Andrzej Kozlowski Jan 25 '12 at 22:02
  • Good enough for me. :-) – Mr.Wizard Jan 25 '12 at 22:07
8

I couldn't resist having a go. This is pretty small:

lcm = Fold[#(#/#2/.{_~_~x_:>x,_->1})&,1,{##}]&
Simon Woods
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  • Marvelous! Just what I was hoping for. Thanks for playing, Simon. I do like your style. :-) – Mr.Wizard Jul 13 '12 at 22:48
  • Simon, I Accepted this answer for a short while, but seeing as I was able to shorten it significantly lifted the Accept. See if you can again beat me. – Mr.Wizard Jul 14 '12 at 00:31