LCM from a ratio and an HCF — Aptitude Question
LCM from a ratio and an HCF: Two numbers are in the ratio 3 : 4 and their HCF is 4. What is their LCM? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
Two numbers are in the ratio 3 : 4 and their HCF is 4. What is their LCM?
Options
- 24
- 36
- 48
- 60
Show the answer and the worked solution
Correct answer: C. 48
Worked solution
- The numbers are 3 × 4 = 12 and 4 × 4 = 16.
- LCM(12, 16) = 48.
Answer: 48.
The idea
When two numbers are in a ratio of coprime terms, the HCF is the common multiplier and the LCM is HCF × product of the ratio terms — here 4 × 3 × 4 = 48.
Shortcut. The numbers are 12 and 16, and their LCM must be divisible by both; 24, 36 and 60 are not divisible by 16, so 48.
Common trap. "24" — it looks right as a multiple of 12 and of both ratio terms 3 and 4, but 24 is not divisible by 16.