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The least common multiple of two numbers is 24 times their greatest common factor. The sum of the least common multiple and the greatest common factor is 450. If one of them is 54, what will be the sum of digits of the second number?

The least common multiple of two numbers is 24 times their greatest common factor. The sum of the least common multiple and the greatest common factor is 450. If one of them is 54, what will be the sum of digits of the second number? Correct Answer 9

Given:

The sum of HCF and LCM is 450

Calculation:

Let be assume LCM and HCF of two numbers is x and y respectively

⇒ x = 24y

⇒ x + y = 450

⇒ 24y + y = 450

⇒ y = 18, x = 432

⇒ Product of two numbers = (HCF × LCM) of the numbers

⇒ The second number = (432 × 18)/54 = 144

⇒ The sum of digits of the number = 1 + 4 + 4 = 9

∴ The required result will be 9.

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