M is the largest three-digit number which divided by 6 and 5 leaves remainder 5 and 3 respectively.  What will be the remainder when M is divided by 11?

4

                   Remainder

        6    →        5

        5    →        3

That number of 23 

                \(\frac{23}{6}\) = 5 remainder

                \(\frac{23}{5}\) = 3 remainder

6, 5 →  LCM  →  30

30 × K + 23 = M

30 × 32 + 23 = M

M = 983

Now  →   \(\frac{983}{11}\) = 4 remainder