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LCM: Difference between revisions
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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]]. | ||
== Extended definition == | |||
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. | |||
<source 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 | |||
</source>{{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 <source lang=apl inline>R←X∧Y</source> is chosen so that both <source lang=apl inline>R÷X</source> and <source lang=apl inline>R÷Y</source> are integers (or [[wikipedia:Gaussian integer|Gaussian integers]], when X and/or Y are [[complex]] numbers). | |||
<source 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 | |||
</source>{{Works in|[[Dyalog APL]]}} | |||
== Description == | |||
The LCM of two numbers is their [[product]] [[divide]]d by the [[GCD]]. | |||
== External links == | |||
=== Documentation === | |||
* [http://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]] | |||