Why is the product of two numbers equal to the product of the greatest common divisor and the least common multiple of the two numbers?
Suppose two numbers are a and B, and their greatest common divisor is a / C,
Then their least common multiple is (A / C) * A / (A / C) * B / (A / C)
B * C is obtained after simplification
So the greatest common divisor times the least common multiple = (A / C) * (b * c) = a * B
So the product of two numbers is equal to the product of the greatest common divisor and the least common multiple of the two numbers