4. Given $P(1,4,5)$ is a fixed point in the rectangular coordinate system $O-x y z$, a plane is drawn through $P$ intersecting the positive half-axes of the three coordinate axes at points $A$, $B$, and $C$ respectively. Then the minimum value of the volume $V$ of all such tetrahedrons $O-A B C$ is $\qquad$
4. 90 .

Let the plane equation be $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$, where the positive numbers $a$, $b$, and $c$ are the intercepts of the plane on the $x$-axis, $y$-axis, and $z$-axis, respectively.
Given that point $P$ lies within plane $ABC$, we have $\frac{1}{a}+\frac{4}{b}+\frac{5}{c}=1$.
From $1=\frac{1}{a}+\frac{4}{b}+\frac{5}{c} \geqslant 3 \sqrt[3]{\frac{1}{a} \times \frac{4}{b} \times \frac{5}{c}}$ $\Rightarrow \frac{1}{6} a b c \geqslant 90$.
When $(a, b, c)=(3,12,15)$, $V$ reaches its minimum value of 90.