Question: Let D be a UFD. An element c in D is a least common multiple (abbreviated Icm) of two elements a and bin D if

Let D be a UFD. An element c in D is a least common multiple (abbreviated Icm) of two elements a and bin D if a | c, b|c and if c divides every element of D that is divisible by both a and b. Show that every two nonzero elements a and b of a Euclidean domain D have an Icm in D.

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