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The least number which when divided by 5, 6, 7, 8 leaves remainder 3, but when divided by 9 leaves no remainder, is:
A1677
B1683
C2523
D3363
Answer & Solution
Correct answer: B. 1683
1. LCM(5,6,7,8) = 840. The number is 840k + 3 for some integer k ≥ 1.
2. We also need (840k + 3) divisible by 9. Check k=1: 843 → 843/9 = 93.67. k=2: 1683 → 1683/9 = 187 exactly.
3. Therefore the least such number is 1683.
_Source: KMAT Karnataka 2021 PYQ Q.37_