Question 154
Determine all triples of positive integers $(x, y, z)$ that satisfy the following system:
$$
\left\{\begin{array}{l}
45 x y^{2}=8 z^{3} \\
x y z\lt 1000
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
45 x y^{2}=8 z^{3} \\
x y z\lt 1000
\end{array}\right.
$$