# 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?

To find the other number, follow the steps mentioned below.

## 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

### Thus, the other number is 80.

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