8. (6 points) Given that $\frac{x}{9}, \frac{y}{15}, \frac{z}{14}$ are all simplest proper fractions, and their product is $\frac{1}{6}$, then $x+y+z=$ $\qquad$
【Solution】Solution: According to the problem, we can get
$$
\frac{x}{9} \times \frac{y}{15} \times \frac{z}{14}=\frac{1}{6}
$$

Then, $x y z=9 \times 15 \times 14 \div 6=3 \times 3 \times 5 \times 7$, based on the characteristics of the simplest proper fraction, we get
$$
x=5, y=7, z=9,
$$

Therefore, $x+y+z=5+7+9=21$.
The answer is: 21.