LCM

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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.

<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

</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 <syntaxhighlight lang=apl inline>R←X∧Y</source> is chosen so that both <syntaxhighlight lang=apl inline>R÷X</source> and <syntaxhighlight lang=apl inline>R÷Y</source> are integers (or 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

</source>

Works in: Dyalog APL

Description

The LCM of two numbers is their product divided by the GCD.

External links

Documentation

APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)
Quad names Index originComparison toleranceMigration levelAtomic vector