The least number which when divided by 5, 6, 7, and 8 leaves the remainder 3. But when divided by 9 leaves no remainder, is:Options :A] 1766B] 1683C] 2327D] 1895

To solve this problem, we need to find the least common multiple (LCM) of 5, 6, 7, and 8. The LCM of these numbers is 840.

This means that our number, when divided by 5, 6, 7, and 8, will leave a remainder of 3. So, we add 3 to the LCM to get 843.

However, the problem also states that the number, when divided by 9, leaves no remainder. This means that our number must be a multiple of 9.

So, we need to find the smallest multiple of 9 that is greater than 843.

We can do this by dividing 843 by 9 to get 93.6667. We round this up to the nearest whole number, which is 94.

We then multiply 94 by 9 to get 846.

However, 846 is not a multiple of 5, 6, 7, and 8. So, we need to keep adding 9 to 846 until we find a number that is a multiple of 5, 6, 7, and 8.

After doing this, we find that the smallest number that meets all these conditions is 1683.

So, the answer is B] 1683.