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)