Mathematics, 26.02.2020 21:34 devenybates
13. The least common multiple of two non-zero integers a and b is the unique positive integer m such that (i) m is a common multiple, i. e. a divides m and b divides m, (ii) m is less than any other common multiple: We denote the least common multiple of a and b by [a, b] or 1cm[a, b], Give a proof by contradiction that if a positive integer n is a common multiple of a and b then [a, b] divides n. [Use the division theorem. If [a, b] does not divide n then n = [a, b]q + r where 0 < r < [a, b]. Now prove that r is a common multiple of a and b.} This means that ab/[a, b] is an integer. Prove that this integer is a common divisor of a and b. Deduce that ab/[a, b] (a, b), t
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13. The least common multiple of two non-zero integers a and b is the unique positive integer m such...
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