# The LCM and HCF of two numbers are 45 and 3 respectively

The LCM and HCF of two numbers are 45 and 3 respectively, their sum is 24, what is their difference?

(a) 2

(b) 4

(c) 6

(d) 8

**Answer: (C) 6 **

**Solution:-**

Let the two numbers be a & b

The LCM and HCF of two numbers are 45 and 3,

Then, the product of two numbers = 45 x 3

ab = 135 …………..(1)

The sum of two numbers (a + b) = 24

Square on both side,

(a + b)^2 = 24^2

a^2 + b^2 + 2 ab = 576

a^2 + b^2 = 576 – 2 x 135 {From equation (1) ab = 135}

a^2 + b^2 = 576 – 270

a^2 + b^2 = 306 ………………. (2)

Difference of two both numbers = a – b

(a – b)^2 = a^2 + b^2 – 2 ab

From equation (1) ab = 1 & equation (2) a^2 + b^2 = 306,

Then, (a – b)^2 = 306 – 2 x 135

(a – b)^2 = 306 – 270

(a – b)^2 = 36

Square root on both side,

a – b = 6

Then, the difference between of two numbers is 6.

Hence, the correct answer is option (C) 6.