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.