Question

The HCF and LCM of 2 numbers are 2 and 60 respectively. If one of the numbers is 14 more than the other, then the smaller number is:
1. 7
2. 5
3. 6
4. 4

Answer 1

Correct Answer - Option 3 : 6

Given:

HCF = 2

LCM = 60

First number = 14 + second number

Concept used:

If 'a' and 'b' are two numbers, then LCM × HCF = a × b

Calculations:

Let the first number be 'a' and second number be 'b'.

LCM × HCF = a × b

⇒ 60 × 2 = (b + 14) × b

⇒ 120 = b² + 14b

⇒ b² + 14b -120 = 0

⇒ (b - 6)(b + 20) = 0

⇒ b = 6

∴ The second number is 6.