4. Given positive integers $a$, $b$, $c$, define the function $f(x, y, z)=$ $a x+b y+c z$, where $x$, $y$, $z \in \mathbf{Z}$. Find the smallest positive integer value of $f(x, y, z)$.
(提示: Let $f_{\text {min }}=a x_{0}+b y_{0}+c z_{0}=d_{0}$. Set $(a, b, c)$ $=d$, obviously $d \mid d_{0}$, thus $d \leqslant d_{0}$. On the other hand, by Bézout's theorem, there exist integers $x, y, z$ such that $a x+b y+c z=d$. Since $d_{0}$ is the smallest, hence $d_{0} \leqslant d$. Therefore, $d_{0}=d$, i.e., $f_{\min }=(a, b, c)$. )