Numbers from a ratio and an LCM — Aptitude Question
Numbers from a ratio and an LCM: Two numbers are in the ratio 4 : 5 and their LCM is 180. What is their sum? Answer and worked solution on CodeKairo.
- Topic: Ratio & Proportion
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Two numbers are in the ratio 4 : 5 and their LCM is 180. What is their sum?
Options
- 72
- 81
- 90
- 99
Show the answer and the worked solution
Correct answer: B. 81
Worked solution
- Let the numbers be 4x and 5x with x their HCF.
- LCM = 20x = 180 → x = 9.
- The numbers are 36 and 45; their sum is 81.
Answer: 81.
The idea
For coprime ratio terms a and b, the LCM of ax and bx is abx. Solving for x recovers both numbers at once.
Shortcut. The sum is 9x and the LCM is 20x, so sum = 180 × 9/20 = 81 — no need to find the numbers.
Common trap. "90" — it looks right as half of 180 and 9 parts of a round 10, but x = 10 gives 40 and 50, whose LCM is 200, not 180.