# LCM of two numbers is 14 times their HCF, sum of LCM and HCF is 600. If one number is 280. What is the other number?

## Answer: If the LCM of two numbers is 14 times their HCF, the sum of LCM and HCF is 600 and If one number is 280, then the other number is 80.

## Explanation:

Let LCM of two numbers be L and HCF of those two numbers be H

According to the question,

L = 14 × H (1)

L + H = 600 (2)

Substitute (1) in (2), we get

14 × H + H = 600

H × (14 + 1) = 600

H × 15 = 600

H = 600 / 15

H = 40

Substitute 40 for H in equation (1)

L = 14 × 40 = 560

We know the formula for two numbers, a and b: LCM (a, b) × HCF (a, b) = a × b

560 × 40 = 280 × b

b = 22400 / 280 = 80