Lines $$l_1^{}$$ and $$l_2^{}$$ both pass through the origin and make first-quadrant angles of $$\frac{\pi}{70}$$ and $$\frac{\pi}{54}$$ radians, respectively, with the positive x-axis. For any line $$l^{}_{}$$, the transformation $$R(l)^{}_{}$$ produces another line as follows: $$l^{}_{}$$ is reflected in $$l_1^{}$$, and the resulting line is reflected in $$l_2^{}$$. Let $$R^{(1)}(l)=R(l)^{}_{}$$ and $$R^{(n)}(l)^{}_{}=R\left(R^{(n-1)}(l)\right)$$. Given that $$l^{}_{}$$ is the line $$y=\frac{19}{92}x^{}_{}$$, find the smallest positive integer $$m^{}_{}$$ for which $$R^{(m)}(l)=l^{}_{}$$.

(第一十届AIME1992 第11题)