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Need help with gcd lcm proof!

  1. Oct 26, 2011 #1
    Let n be a natural number, and let S be the set of all natural numbers that
    divide n.

    For a, ,b in S, let gcd(a, b) = a /\ b and lcm(a, b) = a \/ b. For each x
    in S, let x' denote n/x. Do de Morgan's laws hold for this system?

    (gcd = greatest common divisor, lcm = lowest common multiple)

    This is what I have so far for wanting to show (a /\ b)' = a' \/ b'

    lcm(n/a, n/b) = a' \/ b'

    d = gcd(a, b) = a /\ b.

    d' = n/d

    So somehow I need to show that n/gcd(a, b) = lcm(n/a, n/b)

    From here I've only hit dead-ends.
     
  2. jcsd
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