38. Find the largest number by which each of the fractions $\frac{154}{195}$, $\frac{385}{156}$, and $\frac{231}{130}$ can be divided to yield natural numbers.
38. The numerator of the fraction of the desired number should be the greatest common divisor of the numerators of the given fractions, and the denominator should be the least common multiple of the denominators of these fractions. Since $154=2 \cdot 7 \cdot 11, 385=5 \cdot 7 \cdot 11$ and $231=3 \cdot 7 \cdot 11$, the desired numerator is 77. Since $195=3 \cdot 5 \cdot 13, 156=2^{2} \cdot 3 \cdot 13$ and $130=2 \cdot 5 \cdot 13$, the desired denominator is $2^{2} \cdot 3 \cdot 5 \cdot 13=780$. Therefore, the desired number is $\frac{77}{780}$.