Find the missing number from HCF and LCM: Two numbers have HCF = 15 and LCM = 225. If one number is 75, find the other number.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:For two numbers m and n, the identity m * n = HCF(m, n) * LCM(m, n) lets us find the unknown when one number and both HCF and LCM are known. This avoids trial-and-error completely. Given Data / Assumptions: HCF = 15 LCM = 225 One number = 75 Concept / Approach:Compute the product of HCF and LCM to get m * n, then divide by the known number to obtain the unknown partner. Ensure the quotient is an integer to validate consistency. Step-by-Step Solution: m * n = 15 * 225 = 3375.Given one number is 75, the other is 3375 / 75 = 45. Verification / Alternative check: Check HCF(75, 45) = 15 and LCM(75, 45) = 225; their product is 3375, matching the identity. Why Other Options Are Wrong: 105, 90, 60 do not jointly yield HCF 15 and LCM 225 with 75 under the product identity. Common Pitfalls: Forgetting the product identity or miscalculating 3375/75. Final Answer: 45

Find the missing number from HCF and LCM: Two numbers have HCF = 15 and LCM = 225. If one number is 75, find the other number.

More Questions from Problems on H.C.F and L.C.M

Discussion & Comments