Question

The LCM of two numbers is 495 and HCF is 5. The sum of two numbers are 100. Find the numbers.

Answer 1

Let a & b be the numbers.
ab = 495 × 5 = 2475
a + b = 100
=> a + 2475/a = 100
=> a^2 - 100a + 2475 = 0
=> a^2 - 45a - 55a + 2475 = 0
=> a (a - 45) - 55 (a - 45) = 0
=> (a - 45) (a - 55) = 0
So, a = 45 or, 55
So, two numbers are 45 & 55.