\[1\frac{2}{3} \cdot 1\frac{1}{5} = \frac{3 + 2}{3} \cdot \frac{5 + 1}{5} =\]
\[= \frac{5}{3} \cdot \frac{6}{5} = \frac{5 \cdot 6}{3 \cdot 5} = 2\]