Exercise refer to the following definition.
Definition: The least common multiple of two nonzero integers a and b, denoted lcm(a, b), is the positive integer c such that
a. a | c and b | c
b. for all positive integers m, if a | m and b | m, then c ≤ m.
Exercise
Prove that for all positive integers a and b, gcd(a, b) = lcm(a, b) if, and only if, a = b.
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