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?
- A.
85
- B.
67
- C.
78
- 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.
Let the second number be x.
By the HCF × LCM identity: 95 × x = 5 × 1615.
Compute the right-hand side: 5 × 1615 = 8075.
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.