Let R be a commutative ring with identity, and let a and b be nonzero elements of R. A least common multiple of a and b is an element e of R such that
(i) a|e and b|e, and
(ii) if a|e' and b|e' then e|e'

(b) Deduce that any two nonzero elements in a Euclidean Domain have a least common multiple which is unique up to multiplication by a unit.