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The LCM of two numbers is 28 times their HCF and the sum of their LCM and HCF is 493. The difference of the two numbers is 51. If s is the sum of the two numbers, then what is the sum of digits of s?

The LCM of two numbers is 28 times their HCF and the sum of their LCM and HCF is 493. The difference of the two numbers is 51. If s is the sum of the two numbers, then what is the sum of digits of s? Correct Answer 16

Given:

The LCM of two numbers = 28 × HCF of two numbers

Sum of LCM and HCF = 493

Difference between numbers = 51

Concept:

LCM:- The least common multiple of two numbers is the smallest non zero common number which is a multiple of both the numbers

HCF:- The highest common factor of two or more numbers is the greatest factor that divides the numbers.

LCM × HCF = Product of Numbers

Calculation:

Let the numbers be X and Y and HCF and

LCM of the numbers be p and q respectively

According to the question

q = 28p and p + q = 493

On solving these, we get

⇒ p + 28p = 493

⇒ 29p = 493

⇒ p = 17 and q = 476

Again, According to the concept used

⇒ XY = 476 × 17 = 8092     ----(1)

⇒ X - Y = 51     ----(2)

⇒ X + Y = s     ----(3)

On solving the equations (1) and (2), we get

⇒ X2 - 51X - 8092 = 0

⇒ X = 119, and Y = 68

⇒ By equation (3)

⇒ X + Y = s

⇒ s = 119 + 68 = 187

The sum of the digits of s = 1 + 8 + 7 = 16

∴ The required result will be 16.

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