(10) The smallest positive integer that can be simultaneously expressed as the sum of 9 consecutive integers, the sum of 10 consecutive integers, and the sum of 11 consecutive integers is $\qquad$ .
(10) 495 Hint: Let
$$
\begin{aligned}
t & =l+(l+1)+(l+2)+\cdots+(l+8) \\
& =m+(m+1)+(m+2)+\cdots+(m+9) \\
& =n+(n+1)+(n+2)+\cdots+(n+10),
\end{aligned}
$$

where $n \in \mathbf{N}^{*}$. Then $l=n+2+\frac{2 n+1}{9}, m=\frac{n}{10}+n+1$, so $2 n+1 \equiv 0$ $(\bmod 9), n \equiv 0(\bmod 10)$, then the smallest positive integer $n=40$, i.e.,
$$
t_{\min }=40+41+\cdots+50=495 .
$$