Find two integers whose LCM is 1188 and HCF is 9. Choose the correct pair from the options.
Aptitude
Problems on H.C.F and L.C.M
Difficulty: Easy
Choose an option
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A27, 396
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B9, 27
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C36,99
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DData inadequate
Answer
Correct Answer: 27, 396
Explanation
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