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

Explanation

1. 01

   Let $\operatorname{HCF} = h$, so $\operatorname{LCM} = 14h$.

2. 02

   $h + 14h = 600$, so $h = 40$ and $\operatorname{LCM} = 560$.

3. 03

   Other number = $\frac{40 \times 560}{280} = 80$.

4. 04

   Check: $\operatorname{HCF}(280, 80) = 40$ and $\operatorname{LCM}(280, 80) = 560$.