Curioustab Logo Curioustab
Home » Aptitude » Problems on H.C.F and L.C.M

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

Difficulty: Easy

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
← Previous Question Next Question→

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

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion