10. Let $[a]$ denote the greatest integer not exceeding $a$, then the maximum positive integer solution of the equation $\left[\frac{x}{7}\right]=\left[\frac{x}{8}\right]+1$ is $\qquad$ .
Let $x=56 k+m$, where $0 \leqslant m \leqslant 55$, then we have $8 k+\left[\frac{m}{7}\right]=7 k+\left[\frac{m}{8}\right]+1 \Rightarrow\left[\frac{m}{8}\right]-\left[\frac{m}{7}\right]=k-1$. Clearly, $k=0$ or 1. When $k=0$, $m_{\text {max }}=55$; when $k=1$, $m_{\text {max }}=48$. Therefore, the maximum positive integer solution of the equation is $x=104$.