LCM of 22, 54, 108, 135 and 198 — Aptitude Question
LCM of 22, 54, 108, 135 and 198: Find the LCM of 22, 54, 108, 135 and 198. Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
Find the LCM of 22, 54, 108, 135 and 198.
Options
- 1980
- 2970
- 5940
- 11880
Show the answer and the worked solution
Correct answer: C. 5940
Worked solution
- 22 = 2 × 11, 54 = 2 × 3³, 108 = 2² × 3³, 135 = 3³ × 5, 198 = 2 × 3² × 11.
- Highest powers: 2², 3³, 5, 11.
- LCM = 4 × 27 × 5 × 11 = 5940.
Answer: 5940.
The idea
LCM takes the highest power of every prime present; HCF takes the lowest power of the primes present in all. Writing the factorisations in a column makes both readable at a glance.
Shortcut. Drop 22 and 54, since they divide 198 and 108. Then test options against 108 = 4 × 27: 1980 is not a multiple of 27 and 2970 is not a multiple of 4, while 5940 = 108 × 55 = 135 × 44 = 198 × 30.
Common trap. 2970 — taking the factor 2 only once (2 × 3³ × 5 × 11) and missing the 2² in 108 = 2² × 3³.