What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?

Answer: (b) 1022

A number leaving remainder 2 with each divisor is 2 more than a common multiple of 3, 4, 5 and 6. Their LCM is 60, the first four-digit multiple of 60 is 1020, and so the answer is 1022.

1. LCM(3, 4, 5, 6) = 60.
2. Smallest four-digit multiple of 60: 60 × 17 = 1020 (60 × 16 = 960 has three digits).
3. Required number = 1020 + 2 = 1022.
4. Check: 1022 = 3 × 340 + 2 = 4 × 255 + 2 = 5 × 204 + 2 = 6 × 170 + 2.

Remember · Same remainder r for every divisor: the number = k × LCM + r. Find the smallest k that gives the required size.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error