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The least common multiple of nonzero integers a and b is the smallest positive integer m...

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Advance Math

The least common multiple of nonzero integers a and b is thesmallest positive integer m such that a|m and b|m. It is denoted[a, b], or sometimes [a, b] for short. Prove the following:

1) If a|k and b|k, then [a, b]|k.

2) If gcd(a, b) = 1, then [a, b] =ab

3) If c >0,then [ca, cb] =c·[a, b].

4) If a >0 and b >0,then [a, b] =ab / gcd(a, b).

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