25. Given $x, y, z \in \mathbf{Z}_{+}, [x, y] = 72, [x, z] = 600, [y, z] = 900$, where $[m, n]$ denotes the least common multiple of integers $m$ and $n$. Then the number of ordered integer triples $(x, y, z)$ that satisfy the conditions is $(\quad)$.
(A) 15
(B) 16
(C) 24
(D) 27
(E) 64
25. A.

By the Fundamental Theorem of Arithmetic,
$$
\begin{array}{l}
72=2^{3} \times 3^{2}, 600=2^{3} \times 3 \times 5^{2}, \\
900=2^{2} \times 3^{2} \times 5^{2} . \\
\text { Let } x=2^{a} \times 3^{b} \times 5^{c}, y=2^{d} \times 3^{e} \times 5^{f}, \\
z=2^{g} \times 3^{h} \times 5^{i} .
\end{array}
$$

where $a, b, c, d, e, f, g, h, i \in \mathbf{N}$.
$$
\begin{array}{l}
\text { Then } \max (a, d)=3, \max (b, e)=2, \\
\max (a, g)=3, \max (b, h)=1, \\
\max (c, i)=2, \max (d, g)=2, \\
\max (e, h)=2 .
\end{array}
$$

Since $[x, y]=72 \neq 0(\bmod 5)$, we have
$$
c=f=0 \text {. }
$$

From $\max (d, g)=2, \max (a, d)=3$,
$$
\max (a, g)=3,
$$

we know $a=3$;
From $\max (b, e)=2, \max (b, h)=1$,
$$
\max (e, h)=2 \text {, }
$$

we know $e=2$.
From $\max (b, h)=1$, we know
$$
(b, h)=(1,0),(0,1),(1,1) \text {. }
$$

Since $\max (d, g)=2$, we have
$$
\begin{array}{l}
(d, g) \\
=(2,0),(2,1),(2,2),(0,2),(1,2) .
\end{array}
$$

Therefore, the number of ordered tuples $(a, b, c, d, e, f, g, h, i)$ that satisfy the conditions is $5 \times 3=15$.
Thus, there are 15 tuples $(x, y, z)$.
(Provided by Wu Jianping, translated by Pan Tie)