4. $a, b$ are two positive integers, their least common multiple is 465696. Then the number of such ordered pairs of positive integers $(a, b)$ is ( ) .
(A) 144
(B) 724
(C) 1008
(D) 1155
4. (D).

From $[a, b]=465696=2^{5} \cdot 3^{3} \cdot 7^{2} \cdot 11$, we know that
$$
a=2^{a_{1}} \cdot 3^{a_{2}} \cdot 7^{a_{3}} \cdot 11^{\alpha_{4}}, b=2^{\beta_{1}} \cdot 3^{\beta_{2}} \cdot 7^{\beta_{3}} \cdot 11^{\beta_{4}},
$$

where $\alpha_{i}$ and $\beta_{i}$ are non-negative integers, and
$$
\begin{array}{l}
\max \left(\alpha_{1}, \beta_{1}\right)=5, \max \left(\alpha_{2}, \beta_{2}\right)=3, \\
\max \left(\alpha_{3}, \beta_{3}\right)=2, \max \left(\alpha_{4}, \beta_{4}\right)=1 .
\end{array}
$$

It is easy to see that the pairs $\left(\alpha_{1}, \beta_{1}\right)$ have $2 \times 5+1$ possibilities, $\left(\alpha_{2}, \beta_{2}\right)$ have $2 \times 3+1$ possibilities, $\left(\alpha_{3}, \beta_{3}\right)$ have $2 \times 2+1$ possibilities, and $\left(\alpha_{4}, \beta_{4}\right)$ have $2 \times 1+1$ possibilities.
Therefore, the number of ordered pairs of positive integers $(a, b)$ is
$$
\begin{array}{l}
(2 \times 5+1)(2 \times 3+1)(2 \times 2+1)(2 \times 1+1) \\
=1155 .
\end{array}
$$