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Homework Help: GCD and LCM

  1. Sep 30, 2006 #1
    Is this identity true?

    gcd(a, lcm(b,c)) = lcm(gcd(a,b), gcd(a,c))
  2. jcsd
  3. Sep 30, 2006 #2
    What have you tried so far?

    Have you looked for counter examples or attempted a proof?

    Do you have an idea of how to prove/disprove statements like these?
  4. Sep 30, 2006 #3
    I have already proven it, since the exponents of the all primes of the canonical factorization of a, b and c obeys min(a,max(b,c))=max(min(a,b),min(a,c)).
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