\[\boxed{\mathbf{374}\mathbf{.}}\]
\[1)\ \frac{8 \cdot 14 + 8 \cdot 5}{16 \cdot 57} = \frac{8 \cdot (14 + 5)}{16 \cdot 57} =\]
\[= \frac{8 \cdot 19}{16 \cdot 57} = \frac{1 \cdot 1}{2 \cdot 3} = \frac{1}{6}\]
\[2)\ \frac{13 \cdot 21}{13 \cdot 9 - 13 \cdot 2} =\]
\[= \frac{13 \cdot 21}{13 \cdot (9 - 2)} = \frac{13 \cdot 21}{13 \cdot 7} = 3\]
\[3)\ \frac{18 \cdot 3 + 7 \cdot 18}{90 \cdot 11 - 6 \cdot 90} =\]
\[= \frac{18 \cdot (3 + 7)}{90 \cdot (11 - 6)} = \frac{18 \cdot 10}{90 \cdot 5} =\]
\[= \frac{1 \cdot 2}{5 \cdot 1} = \frac{2}{5}\]