Question

Given two elements a, b in a Euclidean domain R, their least common multiple is

an element c ϵ R such that a | c and b | c and whenever a | x and b | x where x ϵ

R, then c | x. Prove that any two elements a, b in a Euclidean domain R have a

least common multiple [a, b] and further [a, b] = ab / (a, b) where (a, b) denotes

greatest common divisor of a and b.​

Answer 1

Answer:

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