posted by romulo on .
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.