Computes the least common multiple of the input values.


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Inputs/Outputs

  • ci32.png x —

    x is an integer.

  • ci32.png y —

    y is an integer.

  • ii64.png lcm(x,y) —

    lcm(x,y) returns the least common multiple of x and y.

    • lcm(x,y) is the smallest integer m for which there exist integers c and d such that

    x × c = y × d = m

    To compute lcm(x,y), consider the prime factorizations of x and y:

    x = Πi piai y = Πi pibi

    where pi are all the prime factors of x and y. If pi does not occur in a factorization, the corresponding exponent is 0. lcm(x,y) then is given by:

    lcm(x,y) = Πi pimax(ai, bi)

    For example, the prime factorizations of 12 and 30 are given by:

    12 = 2² × 31 × 50 30 = 21 × 31 × 51

    so

    lcm(12,30) = 2² × 31 × 51 = 60