The least common multiple of nonzero integers a and b is the
smallest 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).