my (4) Bonus Question: Let a and b be positive integers. Let a a= Pp and b = p...p be prime decompositions of a and b. H

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My 4 Bonus Question Let A And B Be Positive Integers Let A A Pp And B P P Be Prime Decompositions Of A And B H 1 (22.44 KiB) Viewed 34 times

my (4) Bonus Question: Let a and b be positive integers. Let a a= Pp and b = p...p be prime decompositions of a and b. Here p₁,....pr are prime numbers and n1,...,nr, m1,...,m, are non-negative integers. Recall that lcm(a,b) is the smallest integer such that a and b both divide 1. Let: e₁ = max {n₁, m₁},..., e, = max{n,, mr} Show that: (a) lem(a, b) = pi...p (b) Using (a) show that: axb= lem(a, b) x gcd(a, b)