The LCM and HCF of two numbers is 585 and 13 respectively. Find the difference between the numbers.

Question: The LCM and HCF of two numbers is 585 and 13 respectively. Find the difference between the numbers.

Solution:
Given that,
LCM of numbers = 585
HCF of numbers = 13

Let the number be 13a and 13b where a and b are co-prime.

∴ LCM of 13a and 13b = 13ab

According to question,
13ab = 585
⇒ ab = 585/13
⇒ ab = 45
⇒ ab = 5 × 9
Here, a = 5 and b = 9 or a = 9 and b = 5
∴ First number = 13a = 13 × 5 = 65
And second number = 13b = 13 × 9 = 117

∴ Required difference = 117 - 65 = 52