Find two integers whose LCM is 1188 and HCF is 9. Choose the correct pair from the options.

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

Accepted Answer

Introduction / Context:For two integers m and n, the relation m * n = HCF(m, n) * LCM(m, n) is fundamental. Any candidate pair must satisfy both the product identity and the given HCF. This allows quick validation of each option without exhaustive search. Given Data / Assumptions: LCM = 1188. HCF = 9. We must select a valid pair (order does not matter). Concept / Approach:Check the candidate pair’s HCF and ensure product / HCF equals the stated LCM. If both conditions are satisfied, the pair is valid. If at least one valid pair exists, “Data inadequate” is inappropriate. Step-by-Step Solution: Option A: (27, 396): HCF(27, 396) = 9 (since 396 mod 27 = 18, 27 mod 18 = 9, 18 mod 9 = 0).LCM = (27 * 396) / 9 = 10692 / 9 = 1188. This matches the requirement.Option C: (36, 99): HCF = 9 but LCM = (36*99)/9 = 396, not 1188; invalid. Verification / Alternative check: The identity HCF * LCM = product holds perfectly for (27, 396): 9 * 1188 = 10692 = 27 * 396. Why Other Options Are Wrong: (9, 27) has HCF 9 but LCM 27, not 1188. (36, 99) produces the wrong LCM. “Data inadequate” is wrong because a valid pair exists and is identified. Common Pitfalls: Assuming uniqueness; multiple pairs can exist, but you only need one correct option. Final Answer: 27, 396

Find two integers whose LCM is 1188 and HCF is 9. Choose the correct pair from the options.

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