What is the least common denominator of the fractions (4)/(15),(1)/(20) , and (3)/(8)

To find the least common denominator (LCD) of the fractions $\frac{4}{15}$, $\frac{1}{20}$, and $\frac{3}{8}$, we need to find the least common multiple (LCM) of their denominators: 15, 20, and 8.<br /><br />First, let's find the prime factorization of each number:<br />- 15 = 3 × 5<br />- 20 = 2^2 × 5<br />- 8 = 2^3<br /><br />Next, we find the LCM by taking the highest power of each prime factor that appears in the factorizations:<br />- The highest power of 2 is 2^3.<br />- The highest power of 3 is 3.<br />- The highest power of 5 is 5.<br /><br />Therefore, the LCM of 15, 20, and 8 is:<br />\[ 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 24 \times 5 = 120 \]<br /><br />So, the least common denominator of the fractions $\frac{4}{15}$, $\frac{1}{20}$, and $\frac{3}{8}$ is $\boxed{120}$.