The product of the LCM and HCF of two numbers is 24. The

Home » Aptitude » LCM and HCF » Question

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

1. 8 and 6
2. 8 and 10
3. 2 and 4
4. 6 and 4

Correct Option: D

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.