Explain how [a,b]= ab/(a,b) this combined to compute the least common multiple?

I need explanation how this inequality can be combined with the Euclidean algorithm to provide an efficient means of computing the lcm of a and b without using prime factorizations.[a,b] stands for lcm of a and b; (a,b) stands for gcd; ab stands for the product of a and b, the positive integers.