10. (5 points) It is known that the denominators of three simplest proper fractions are 6, 15, and 20, respectively, and their product is $\frac{1}{30}$. Among these three simplest proper fractions, the largest number is $\qquad$
【Solution】Solution: According to the problem, let these three numbers be $\frac{a}{6}, \frac{b}{15}, \frac{c}{20}$, since $\frac{a}{6} \times \frac{b}{15} \times \frac{c}{20}=\frac{1}{30}$,

then $a b c=60$.
Decompose 60: $60=2 \times 2 \times 3 \times 5$,
Since all three fractions are proper fractions,
thus $c=3, a=5, b=4$.
Therefore, the largest is $\frac{5}{6}$.
In conclusion, the largest fraction is $\frac{5}{6}$.
The answer is: $\frac{5}{6}$.