What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3?
Answer & explanation
Answer: (c) 1083
A number leaving remainder 3 with each divisor is 3 more than a common multiple of them. LCM(6, 9, 12, 15, 18) = 180, and the first multiple of 180 that gives a number above 1000 is 1080, so the answer is 1083.
- LCM(6, 9, 12, 15, 18) = 180.
- The number must be of the form 180k + 3.
- 180 × 5 + 3 = 903 is below 1000; 180 × 6 + 3 = 1083 is the first above it.
- Check: 1083 − 3 = 1080 is divisible by 6, 9, 12, 15 and 18.
Remember · Same remainder r for several divisors: the number = k × LCM + r.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·