## Question

`What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?`

`What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?`

A. 1108

B. 3363

C. 2007

D. 1683

**Answer: D. 1683**

**Solution:**

Take 1108. This is not even divisible by 9. Hence this is not the answer.

Take 3363. This is not even divisible by 9. Hence this is not the answer.

Take 2007. This is divisible by 9.

2007 ÷ 5 = 401, remainder = 2 . Hence this is not the answer

Take 1683. This is divisible by 9.

1683 ÷ 5 = 336, remainder = 3

1683 ÷ 6 = 280, remainder = 3

1683 ÷ 7 = 240, remainder = 3

1683 ÷ 8 = 210, remainder = 3**Hence 1683 is the answer.**

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