Given nonzero integers a and b, establish the following facts concerning 1cm(a, b).
(a) gcd(a, b) = lcm(a, b) if and only if a = ±b.
(b) If k > 0, then lcm(ka, kb) = k 1cm(a, b).
(c) If m is any common multiple of a and b, then lcm(a, b) | m.
[Hint: Put t = lcm(a, b) and use the Division Algorithm to write m = qt + r, where 0 ≤ r<t. Show that r is a common multiple of a and b.]
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