Question

The HCF and LCM of two numbers are 12 and 72 respectively. If the sum of the two numbers is 60, then one of the two numbers will be:
1. 72
2. 60
3. 24
4. 12

Answer 1

Correct Answer - Option 3 : 24

Given:

HCF = 12

LCM = 72

Sum of number = 60

Concept used:

Product of number = HCF × LCM

Calculation:

Let the 1st number be x

2nd number will be (60 - x)

Product of number = HCF × LCM

⇒ x × (60 - x) = 12 × 72

⇒ 60x - x² = 864

⇒ x² - 60x + 864 = 0

⇒ x² - 24x - 36x + 864 = 0

⇒ x(x - 24) - 36(x - 24) = 0

⇒ (x - 24)(x - 36) = 0

⇒ (x - 24) = 0 or (x - 36) = 0

⇒ x = 24 or x = 36                

∴ The one of the number is 24.