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Math Help - prove gcd and lcm

  1. #1
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    prove gcd and lcm

    Show that if a and b are positive integers, then there are divisors c of a and d of b with gcd(c,d)=1 and cd=lcm[a,b]
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  2. #2
    Senior Member TriKri's Avatar
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    Quote Originally Posted by mandy123 View Post
    Show that if a and b are positive integers, then there are divisors c of a and d of b with gcd(c,d)=1 and cd=lcm[a,b]
    Set c = a/gcd(a, b), this makes sure c and b have no common divisors. And with d = b, c and d have no in common either.

    So, gcd(c, d) = 1.

    And, since lcm(x, y) can be defined as x*y/gcd(x, y), cd=a/gcd(a, b)*b = lcm(a, b)
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