A number when divided successively by 6, 7 and 8 . it leaves the respective remainders of 3,5 and 4 . What will be the last remaindr when such a least possible number is divided successively by 8, 7 and 6 ?

Explanation

To solve the problem, we need to find a number \( N \) that, when divided by 6, 7, and 8, leaves remainders of 3, 5, and 4 respectively. Then, we will find the last remainder when this number \( N \) is divided successively by 8, 7, and 6.

### Step 1: Set up the equations based on the given conditions

From the problem, we have the following equations based on the division and remainders:

1. \( N \equiv 3 \mod 6 \)
2. \( N \equiv 5 \mod 7 \)
...