Find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.
Question and options
Find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.
- 1677
- 1683
- 2523
- 3363
Answer and explanation
Correct answer: B - 1683
Number = 840k + 3 (LCM of 5,6,7,8 is 840). 840 leaves remainder 3 mod 9, so 3k + 3 must be divisible by 9, giving k = 2: 1683 = 9 x 187, the least such number.
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CUSAT CAT Five-Year LL.B.
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