Divisible by both 9 and 11 — Number System Aptitude Question
Divisible by both 9 and 11: What is the largest three-digit number divisible by both 9 and 11? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
What is the largest three-digit number divisible by both 9 and 11?
Options
- 891
- 909
- 990
- 999
Show the answer and the worked solution
Correct answer: C. 990
Worked solution
- Since 9 and 11 are coprime, the number must be divisible by 99.
- 999 ÷ 99 = 10 remainder 9, so the largest multiple is 999 − 9 = 990.
- Check: 990 = 9 × 110 = 11 × 90. ✓
Answer: 990.
The idea
For coprime divisors the LCM is simply their product. If they shared a factor you would have to compute the LCM properly rather than multiply.
Shortcut. Test from the top: 999 fails 11 (alternating sum 9), while 990 has digit sum 18 and alternating sum 0, so it passes both tests.
Common trap. 999 — the largest three-digit number and a multiple of 9, but 999 ÷ 11 leaves 9.