6. Let a, b € N, not both 0, and let [a, b] be the smallest positive integer

that is a multiple of both a and b. (This is the least common multiple.)

(a) Prove that ab/[a, b] is a common divisor of a and b.

(b) Prove that ab/(a, b) is common multiple of a and b.

(c) Use parts (a) and (b) and the definitions of greatest common divisor

and least common multiple to prove that ab = (a, b) [a, b].