# Euclidean Rings and GCD

If the least common multiple of a and b in the Euclidean ring R is denoted by [a,b],

prove that

[a,b] = ab/(a, b) where (a, b) is the greatest common divisor of a and b.

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Modern Algebra

Ring Theory (XVIII)

Euclidean Ring

Greatest Common Divisor

Least Common Multiple

By:- Thokchom Sarojkumar Sinha

If the least common multiple of and in the Euclidean ring is denoted by ,

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#### Solution Summary

Euclidean Rings and GCD are investigated. The solution is detailed and well presented.