Two numbers have HCF 5 and LCM 1615. If one of them is 95, what is the second…

2023

Two numbers have HCF 5 and LCM 1615. If one of them is 95, what is the second number?

  1. A.

    85

  2. B.

    67

  3. C.

    78

  4. D.

    90

Show answer & explanation

Correct answer: A

For any two positive integers, the product of the numbers always equals the product of their HCF and LCM: First Number × Second Number = HCF × LCM. This identity holds regardless of what the specific numbers are.

  1. Let the second number be x.

  2. By the HCF × LCM identity: 95 × x = 5 × 1615.

  3. Compute the right-hand side: 5 × 1615 = 8075.

  4. Solve for x: x = 8075 ÷ 95 = 85.

Cross-check: 95 = 5 × 19 and 85 = 5 × 17, so HCF(95, 85) = 5 as required. Also LCM(95, 85) = (95 × 85) ÷ 5 = 8075 ÷ 5 = 1615, matching the given LCM — confirming 85 is correct.

Explore the full course: Cognizant Preparation