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# | {{Built-in|LCM|∧}} is a [[dyadic]] [[scalar function]] which returns the '''[[wikipedia:Least common multiple|Least Common Multiple]]''' of two integer arguments. It is an extension of [[And]] which maintains the same results on [[Boolean]] arguments and the same [[identity element]] 1, in the same way that [[GCD]] extends [[Or]]. | ||
== Examples == | |||
For positive integer arguments, the least common multiple is the smallest positive number which is divisible by both numbers. If one of the arguments is zero, the LCM function returns zero. | |||
<syntaxhighlight lang=apl> | |||
∘.∧⍨ 0,⍳10 | |||
0 0 0 0 0 0 0 0 0 0 0 | |||
0 1 2 3 4 5 6 7 8 9 10 | |||
0 2 2 6 4 10 6 14 8 18 10 | |||
0 3 6 3 12 15 6 21 24 9 30 | |||
0 4 4 12 4 20 12 28 8 36 20 | |||
0 5 10 15 20 5 30 35 40 45 10 | |||
0 6 6 6 12 30 6 42 24 18 30 | |||
0 7 14 21 28 35 42 7 56 63 70 | |||
0 8 8 24 8 40 24 56 8 72 40 | |||
0 9 18 9 36 45 18 63 72 9 90 | |||
0 10 10 30 20 10 30 70 40 90 10 | |||
</syntaxhighlight>{{Works in|[[Dyalog APL]]}} | |||
While the mathematical definition of LCM does not cover non-integers, some implementations accept them as arguments. In this case, the return value of <syntaxhighlight lang=apl inline>R←X∧Y</syntaxhighlight> is chosen so that both <syntaxhighlight lang=apl inline>R÷X</syntaxhighlight> and <syntaxhighlight lang=apl inline>R÷Y</syntaxhighlight> are integers (or [[wikipedia:Gaussian integer|Gaussian integers]], when X and/or Y are [[complex]] numbers). | |||
<syntaxhighlight lang=apl> | |||
0.9∧25÷6 | |||
112.5 | |||
112.5÷0.9(25÷6) | |||
125 27 | |||
2J2∧3J1 | |||
6J2 | |||
6J2÷2J2 3J1 | |||
2J¯1 2 | |||
</syntaxhighlight>{{Works in|[[Dyalog APL]]}} | |||
== Description == | |||
The LCM of two numbers is their [[product]] [[divide]]d by the [[GCD]]. | |||
== External links == | |||
=== Documentation === | |||
* [https://help.dyalog.com/17.1/#Language/Primitive%20Functions/And%20Lowest%20Common%20Multiple.htm Dyalog] | |||
* J [https://www.jsoftware.com/help/dictionary/d111.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/stardot#dyadic NuVoc] | |||
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]] | |||