Question : The least number, which when divided by 5, 6, 7 and 8 leaves a remainder of 3, but when divided by 9, leaves no remainder, is:
Option 1: 1677
Option 2: 1683
Option 3: 2523
Option 4: 3363
Correct Answer: 1683
Solution :
The LCM of 5, 6, 7, and 8 is 840.
If 3 is added to 840 it becomes 843, which, when divided by 5, 6, 7, and 8, leaves the remainder of 3.
843 is not completely divisible by 9 and hence, we will take multiples of 840
The required number will be in the form of 840K + 3 (where K is any integer)
After putting K = 2, we get 1683 which is completely divisible by 9.
Hence, the correct answer is 1683.
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