Two numbers have HCF + LCM = 403 and also LCM = 12 times HCF. If one number is 93, find the other number.

Question

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

Accepted Answer

Introduction / Context:This problem blends two key identities: (i) for two integers m and n, HCF * LCM = m * n, and (ii) here an extra relation LCM = 12 * HCF plus their sum. Using these, we can compute HCF and LCM first, then use the product identity to find the unknown integer directly. Given Data / Assumptions: H + L = 403. L = 12H. Known number = 93. Concept / Approach:From L = 12H and H + L = 403, solve for H, L. Then use m * n = H * L to find the partner of 93: other = (H * L) / 93. Ensure the result is an integer to be consistent with integer inputs. Step-by-Step Solution: H + 12H = 403 ⇒ 13H = 403 ⇒ H = 31.Thus L = 12 * 31 = 372.Product m * n = H * L = 31 * 372 = 11532.Given one number is 93, the other = 11532 / 93 = 124. Verification / Alternative check: Check: HCF(93,124) = 31 and LCM = (93*124)/31 = 372. Sum 31 + 372 = 403 and 372 = 12 * 31, all satisfied. Why Other Options Are Wrong: 115, 122, 138 do not yield HCF 31 and LCM 372 with 93 under the product relation. Common Pitfalls: Mistakes in dividing 11532 by 93 or in solving 13H = 403. Final Answer: 124

Two numbers have HCF + LCM = 403 and also LCM = 12 times HCF. If one number is 93, find the other number.

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