Suppose you have two numbersPandQ. Explain carefully why the product of their greatest commondivisor and their least common multiple is equal toP Q.

Greatest common divisor (P,Q) ×  Least common multiple (P,Q) = PQ

Step-by-step explanation:

Given: Two numbers are P and Q

To prove: product of their greatest common divisor and their least common multiple is equal to PQ

Solution:

Consider the following relation:

Greatest common divisor (P,Q) ×  Least common multiple (P,Q) = Product of numbers P and Q

Therefore,

Greatest common divisor (P,Q) ×  Least common multiple (P,Q) = PQ