1. The problem is to find the lowest common denominator (LCD) of the fractions $\frac{9}{20}$ and $\frac{8}{15}$.\n\n2. The denominators are 20 and 15. We need to find the least common multiple (LCM) of these two numbers because the LCD is the LCM of the denominators.\n\n3. Prime factorize each denominator:\n- $20 = 2^2 \times 5$\n- $15 = 3 \times 5$\n\n4. To find the LCM, take the highest powers of all prime factors present:\n- For 2: highest power is $2^2$\n- For 3: highest power is $3^1$\n- For 5: highest power is $5^1$\n\n5. Multiply these together to get the LCM:\n$$\text{LCM} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$$\n\n6. Therefore, the lowest common denominator of $\frac{9}{20}$ and $\frac{8}{15}$ is $60$.