Prove that the greatest common divisor of two positive integ

Prove that the greatest common divisor of two positive integers divides their least common multiple.

Solution

Let two positive integer m = ad and n = bd.

then Greatest common divisor(GCD) of m and n = d

and Least common multiple(LCM) of m and n = abd

hence d is common factor between LCM and GCD

Then it is true that greatest common divisor of two positive integers divides their least common multiple.