The product of the LCM and HCF of two numbers is 24. The difference of the two numbers is 2. Find the numbers:

6, 4

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.