1. The problem asks for the least common denominator (LCD) of the fractions $\frac{3}{5}$ and $\frac{1}{10}$.\n\n2. The denominator is the bottom number of a fraction, and the LCD is the smallest number that both denominators divide into evenly.\n\n3. The denominators here are 5 and 10.\n\n4. To find the LCD, list the multiples of each denominator:\n- Multiples of 5: 5, 10, 15, 20, ...\n- Multiples of 10: 10, 20, 30, 40, ...\n\n5. The smallest common multiple is 10.\n\n6. Therefore, the least common denominator of $\frac{3}{5}$ and $\frac{1}{10}$ is $10$.