The LCM of two numbers is 20 times their HCF. The sum of HCF and LCM is 2520.…

2023

The LCM of two numbers is 20 times their HCF. The sum of HCF and LCM is 2520. If one of the numbers is 480, then what is the other number?

  1. A.

    400

  2. B.

    480

  3. C.

    520

  4. D.

    600

Show answer & explanation

Correct answer: D

For two numbers, the product of the numbers always equals the product of their HCF and LCM: First number × Second number = HCF × LCM. When the LCM is given as a multiple of the HCF (here, LCM = 20 × HCF), express both in terms of a single variable using their sum.

  1. Let HCF = x, so LCM = 20x (since the LCM is 20 times the HCF).

  2. Using the given sum: x + 20x = 2520, that is, 21x = 2520, so x = 120.

  3. Therefore, HCF = 120 and LCM = 20 × 120 = 2400.

  4. Apply the identity First number × Second number = HCF × LCM: 480 × (other number) = 120 × 2400.

  5. Solving, the other number = (120 × 2400) ÷ 480 = 600.

Check: 480 = 25 × 3 × 5, and 600 = 23 × 3 × 52, so their HCF is 23 × 3 × 5 = 120 and their LCM is 25 × 3 × 52 = 2400 — matching the values used above, and 120 + 2400 = 2520 as given.

So the other number is 600.

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