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The least number which when divided by 5, 6, 7, 8 and leaves remainder 3. But when the same number is divided by 9, it leaves no remainder. The number is

The least number which when divided by 5, 6, 7, 8 and leaves remainder 3. But when the same number is divided by 9, it leaves no remainder. The number is Correct Answer 1683

In this case we will evaluate the LCM of 5, 6, 7, 8 which is 840.

It is given that the least number which when divided by 5, 6, 7, 8 leaves a remainder 3.Hence the number should be 3 more than their LCM, in order to leave such remainder.

If we take the required number as 843 and add 8 + 4 + 3, we get 15 and 15 is not divisible by 9. We get to know that the number isn’t 843.

∴ We will take the required number as (840 × k + 3) where k is the least positive integer. This will make the entire number divisible by 9 also, as required in the question.

Now the least value of k for which (840 × k + 3) is divisible by 9 is 2.

∴ The required number is (840 × 2 + 3) or 1683.

We can also check that 1 + 6 + 8 + 3 is 18 which is divisible by 9.

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