Greatest four-digit common multiple — Aptitude Question
Greatest four-digit common multiple: What is the greatest four-digit number divisible by 15, 25, 40 and 75? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the greatest four-digit number divisible by 15, 25, 40 and 75?
Options
- 9000
- 9200
- 9600
- 9800
Show the answer and the worked solution
Correct answer: C. 9600
Worked solution
- 15 = 3 × 5, 25 = 5², 40 = 2³ × 5, 75 = 3 × 5² → LCM = 2³ × 3 × 5² = 600.
- 9999 ÷ 600 = 16 remainder 399.
- Greatest multiple = 9999 − 399 = 9600.
Answer: 9600.
The idea
Divisible by several numbers means divisible by their LCM. Reduce to one divisor first, then it is an ordinary largest-multiple question.
Shortcut. Every option ends in 00 with its last three digits divisible by 8, so only the factor 3 in the LCM 600 decides. Digit sums 9, 11, 15, 17 leave 9000 and 9600, and the larger wins.
Common trap. 9800 — the largest option and divisible by 25 and 40, but its digit sum 17 fails 3, so it is not a multiple of 15 or 75.