Question :

The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers.Submitted on 3/3/2024 | Answered by Vandana Rana

Answer :

Let the numbers be p and (p + 2)
∴ Product of numbers = HCF × LCM
⇒ p (p + 2) = 24
⇒ p² + 2p – 24 = 0
⇒ p² + 6p – 4p – 24 = 0
⇒ p (p + 6) – 4 (p + 6) = 0
⇒ (p – 4) (p + 6) = 0
⇒ p = 4 or p = – 6
Numbers = p = 4 and p + 2 = 4 + 2 = 6.
∴ Numbers are 4 and 6.