Question 152
Determine all triples of positive integers $ (x, y, z) $ that satisfy the following system:
$$
\left\{\begin{array}{l}
45 x y^{2}=8 z^{3} \\
x y z\lt 1000
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
45 x y^{2}=8 z^{3} \\
x y z\lt 1000
\end{array}\right.
$$