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March 24, 2017

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If a and b are positive integers, and m=lcm(a,b), explain why m divides any common multiple of a and b.

The answer is in the definition of lcm:]

the smallest multiple that is exactly divisible by every member of a set of numbers.

So if m is divisble by a or b, then ab divides into m evenly. Then any ab product multiplied by an interger n (nab) is divided evenly by m.

Thank you very much Bob Pursley!! A gent and a scholar.

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