10. A number lies between 2013 and 2156, and when divided by $5$, $11$, and $13$, the remainders are the same. The largest possible remainder is $\qquad$ _.
【Analysis】This number minus the remainder results in a common multiple of $5$, $11$, and $13$. Since the divisor includes 5, the remainder can be at most 4. 
Therefore, this number minus the remainder is at least 2009 and at most 2156 (i.e., when the remainder is 0). $[5,11,13]=715$, and $715 \times 3=2145$. Thus, we find that 2149 is between 2013 and 2156, and when divided by $5$, $11$, and $13$, the remainder is the same and the largest, which is 4. 
Therefore, the answer is 4.