The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is = ?

LCM = 495 HCF = 5 ( given ) ∴ Let numbers are = 5x and 5y ∴ LCM = 5xy ⇒ 5xy = 495 ⇒ xy = 99 ∴ Possible co-prime factors are 1, 99 9, 11 ∴ Possible numbers are 5x, 5y 45, 55 5, 495 Now given that sum of numbers = 100 So, required numbers are = (45, 55) ∴ Difference of numbers = 55 - 45 = 10