See the attached file.
This solution is comprised of a detailed explanation of least common multiple (l.c.m.) of a and b in R. It contains step-by-step explanation of the problem that if R is a unique factorization domain and if a,b are in R, then a and b have a least common multiple (l.c.m.) in R..
Notes are also given at the end.
Solution contains detailed step-by-step explanation.