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Math Help - Prove that gcd(a,b) divides lcm[a,b]

  1. #1
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    Prove that gcd(a,b) divides lcm[a,b]

    Prove that gcd(a,b) divides lcm[a,b].
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  2. #2
    Super Member Bacterius's Avatar
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    Hello,

    lcm(a, b) = \frac{|a \times b|}{gcd(a, b)}.

    Can you conclude now ?
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by tarheelborn View Post
    Prove that gcd(a,b) divides lcm[a,b].
    We know that a\mid [a,b] and (a,b)\mid a and so (a,b)\mid [a,b]

    Quote Originally Posted by Bacterius View Post
    Hello,

    lcm(a, b) = \frac{|a \times b|}{gcd(a, b)}.

    Can you conclude now ?
    That is kind of taken to not be known.
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  4. #4
    Super Member Bacterius's Avatar
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    That is kind of taken to not be known.
    Sorry, English not being my first language, I don't grasp the meaning of this sentence
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  5. #5
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Bacterius View Post
    Sorry, English not being my first language, I don't grasp the meaning of this sentence
    It's cool. Clearly the problem is trivial if that fact is known, so it would probably be assumed the OP isn't aware of that fact.
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  6. #6
    Super Member Bacterius's Avatar
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    Oh, right. Well, I think you are right, and I actually think that I ruined everything in the sense that this problem was probably given for him to work out this formula ... that will teach me !
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