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Homework Help: Number theory proof - gcf and lcm

  1. May 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove gcd(lcm(a, b), c) = lcm(gcd(a, c), gcd(b, c))

    I've tried coming up with a way to even rewrite it but I'm not really able to do it.
  2. jcsd
  3. May 8, 2012 #2

    I like Serena

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    Homework Helper

    Hi roto! :smile:

    Easiest is to set up a couple of Venn diagrams with the supposed prime factors in it.
    An lcm is a union and a gcd is an intersection.

    Do you know how to do that?
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