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Exercise refer to the following
Chapter 4, Problem 27E(choose chapter or problem)
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 thata. a | c and b | c________________b. for all positive integers m, if a | m and b | m, then c ? m.ExerciseProve that for all integers a and b, gcd(a, b) | lcm(a, b).
Questions & Answers
QUESTION:
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 thata. a | c and b | c________________b. for all positive integers m, if a | m and b | m, then c ? m.ExerciseProve that for all integers a and b, gcd(a, b) | lcm(a, b).
ANSWER:Solution : Here, we need to prove that for all integers a and b, gcd(a, b) | lcm(a, b).Step 1. Let gcd(a,b) = d then ………….(1)