Difference between revisions of "LCM"
m (→Extended definition: Change the heading to Examples) 
m (Text replacement  "http://help.dyalog.com" to "https://help.dyalog.com") 

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=== Documentation ===  === 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]  * J [https://www.jsoftware.com/help/dictionary/d111.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/stardot#dyadic NuVoc]  
{{APL builtins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]]  {{APL builtins}}[[Category:Primitive functions]][[Category:Scalar dyadic functions]] 
Latest revision as of 14:28, 14 July 2020
∧

LCM (∧
) is a dyadic scalar function which returns the 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.
∘.∧⍨ 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
While the mathematical definition of LCM does not cover nonintegers, some implementations accept them as arguments. In this case, the return value of R←X∧Y
is chosen so that both R÷X
and R÷Y
are integers (or Gaussian integers, when X and/or Y are complex numbers).
0.9∧25÷6
112.5
112.5÷0.9(25÷6)
125 27
2J2∧3J1
6J2
6J2÷2J2 3J1
2J¯1 2
Description
The LCM of two numbers is their product divided by the GCD.