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Math Help - common divisor proof

  1. #1
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    common divisor proof

    Q: ab/[a,b] is an integer. Prove that this integer is a common divisor of a and b. Deduce that ab/[a,b] is less than or equal to (a,b), the greatest common divisor of a and b.

    ([a,b]=lowest common multiple of a and b)




    I have no idea how to start this one :S
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  2. #2
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    LCM and GCD

    Hello dlbsd
    Quote Originally Posted by dlbsd View Post
    Q: ab/[a,b] is an integer. Prove that this integer is a common divisor of a and b. Deduce that ab/[a,b] is less than or equal to (a,b), the greatest common divisor of a and b.

    ([a,b]=lowest common multiple of a and b)




    I have no idea how to start this one :S
    You just need to prove that ab = [a, b].(a, b). The proof is here, Least Common Multiple -- from Wolfram MathWorld, about half-way down, from (10) to (14).

    Grandad
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