Counting common multiples in a range — Aptitude Question
Counting common multiples in a range: How many numbers between 200 and 600 are divisible by 4, 5 and 6? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
How many numbers between 200 and 600 are divisible by 4, 5 and 6?
Options
- 5
- 6
- 7
- 8
Show the answer and the worked solution
Correct answer: B. 6
Worked solution
- LCM(4, 5, 6) = 60.
- Multiples of 60 strictly between 200 and 600: 240, 300, 360, 420, 480, 540.
- That is 6 numbers.
Answer: 6.
The idea
Convert to a single divisor with the LCM, then count with ⌊upper/d⌋ − ⌊lower/d⌋, checking whether the endpoints themselves are meant to be included.
Shortcut. LCM 60: ⌊600/60⌋ − ⌊200/60⌋ = 10 − 3 = 7 counts 600 itself, and 'between' excludes it, leaving 6.
Common trap. 7 — counting 600 as one of the numbers; 'between 200 and 600' shuts out the endpoint.