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There are two numbers A and B and the sum of the square of both the numbers is 2197 and the multiplication of LCM and HCF of both the numbers is 1014, then LCM of A and B is how much times of their HCF?

There are two numbers A and B and the sum of the square of both the numbers is 2197 and the multiplication of LCM and HCF of both the numbers is 1014, then LCM of A and B is how much times of their HCF? Correct Answer 6

Given:

A2 + B2 = 2197

LCM × HCF = 1014

Formula Used:

First number × Second number = HCF × LCM

(A + B)2 = A2 + B2 + 2AB

(A – B)2 = A2 + B2 – 2AB

Calculation:

AB = 1014

(A + B)2 = 2197 + 2 × 1014 = 4225

⇒ A + B = 65      ----(i)

(A – B)2 = 2197 – 2 × 1014 = 169

⇒ A – B = 13      ----(ii)

From (i) and (ii):

A = 39 and B = 26

⇒ LCM of A and B = 78

⇒ HCF of A and B = 13

∴ Required answer = 78/13 = 6

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