HCF, LCM and the other number — Aptitude Question
HCF, LCM and the other number: The HCF of two numbers is 12 and their LCM is 360. If one of the numbers is 72, what… Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 60 seconds
Question
The HCF of two numbers is 12 and their LCM is 360. If one of the numbers is 72, what is the other?
Options
- 48
- 60
- 90
- 120
Show the answer and the worked solution
Correct answer: B. 60
Worked solution
- For any two numbers, HCF × LCM = product of the numbers.
- So the other number = (12 × 360) ÷ 72 = 4320 ÷ 72 = 60.
- Check: HCF(72, 60) = 12 and LCM(72, 60) = 360. ✓
Answer: 60.
The idea
HCF × LCM = a × b holds for exactly two numbers (not three or more). When three of the four quantities are known, the fourth is one division away.
Shortcut. The other number must be a multiple of 12 that divides 360: 48 and 90 fail at once, and 120 shares 24 with 72, leaving 60.
Common trap. 120 — a multiple of 12 whose LCM with 72 is indeed 360, but HCF(72, 120) = 24, not 12.