# 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

Anurag Mishra Professor Asked on 29th February 2016 in

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.

Anurag Mishra Professor Answered on 1st March 2016.