1. Find the lowest common denominator (LCD) for $\frac{3}{4}$ and $\frac{3}{16}$. 2. Find the LCD for $\frac{9}{16}$ and $\frac{7}{32}$. 3. Find the LCD for $\frac{3}{64}$, $\frac{9}{16}$, and $\frac{1}{2}$. 4. Find the LCD for $\frac{5}{16}$, $\frac{7}{32}$, and $\frac{11}{12}$. 5. Find the LCD for $\frac{3}{16}$, $\frac{1}{3}$, and $\frac{1}{4}$. 6. Find the LCD for $\frac{7}{27}$, $\frac{33}{36}$, and $\frac{5}{23}$. 7. Find the LCD for $\frac{7}{64}$, $\frac{43}{88}$, and $\frac{51}{92}$. 8. Find the LCD for $\frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{4}$, and $\frac{1}{6}$. 9. Find the LCD for $\frac{1}{12}$, $\frac{1}{10}$, $\frac{3}{16}$, and $\frac{7}{24}$. 10. Find the LCD for $\frac{5}{16}$, $\frac{4}{5}$, $\frac{5}{24}$, $\frac{3}{4}$, $\frac{5}{8}$, and $\frac{7}{15}$. **Step 1:** Recall that the lowest common denominator (LCD) is the least common multiple (LCM) of the denominators. **Step 2:** Find the prime factorization of each denominator. **Step 3:** For each set, find the LCM by taking the highest powers of all prime factors. **Step 4:** Calculate the LCD for each problem. --- 1. Denominators: 4 = $2^2$, 16 = $2^4$. LCM = $2^{\max(2,4)} = 2^4 = 16$. LCD = 16. --- 2. Denominators: 16 = $2^4$, 32 = $2^5$. LCM = $2^{\max(4,5)} = 2^5 = 32$. LCD = 32. --- 3. Denominators: 64 = $2^6$, 16 = $2^4$, 2 = $2^1$. LCM = $2^{\max(6,4,1)} = 2^6 = 64$. LCD = 64. --- 4. Denominators: 16 = $2^4$, 32 = $2^5$, 12 = $2^2 \times 3$. LCM = $2^{\max(4,5,2)} \times 3^{\max(0,0,1)} = 2^5 \times 3 = 32 \times 3 = 96$. LCD = 96. --- 5. Denominators: 16 = $2^4$, 3 = $3$, 4 = $2^2$. LCM = $2^{\max(4,0,2)} \times 3^{\max(0,1,0)} = 2^4 \times 3 = 16 \times 3 = 48$. LCD = 48. --- 6. Denominators: 27 = $3^3$, 36 = $2^2 \times 3^2$, 23 = $23$ (prime). LCM = $2^{\max(0,2,0)} \times 3^{\max(3,2,0)} \times 23^{\max(0,0,1)} = 2^2 \times 3^3 \times 23 = 4 \times 27 \times 23 = 2484$. LCD = 2484. --- 7. Denominators: 64 = $2^6$, 88 = $2^3 \times 11$, 92 = $2^2 \times 23$. LCM = $2^{\max(6,3,2)} \times 11^{\max(0,1,0)} \times 23^{\max(0,0,1)} = 2^6 \times 11 \times 23 = 64 \times 11 \times 23 = 16192$. LCD = 16192. --- 8. Denominators: 2 = $2$, 3 = $3$, 4 = $2^2$, 6 = $2 \times 3$. LCM = $2^{\max(1,0,2,1)} \times 3^{\max(0,1,0,1)} = 2^2 \times 3 = 4 \times 3 = 12$. LCD = 12. --- 9. Denominators: 12 = $2^2 \times 3$, 10 = $2 \times 5$, 16 = $2^4$, 24 = $2^3 \times 3$. LCM = $2^{\max(2,1,4,3)} \times 3^{\max(1,0,0,1)} \times 5^{\max(0,1,0,0)} = 2^4 \times 3 \times 5 = 16 \times 3 \times 5 = 240$. LCD = 240. --- 10. Denominators: 16 = $2^4$, 5 = $5$, 24 = $2^3 \times 3$, 4 = $2^2$, 8 = $2^3$, 15 = $3 \times 5$. LCM = $2^{\max(4,0,3,2,3,0)} \times 3^{\max(0,0,1,0,0,1)} \times 5^{\max(0,1,0,0,0,1)} = 2^4 \times 3 \times 5 = 16 \times 3 \times 5 = 240$. LCD = 240. --- **Final answers:** 1. 16 2. 32 3. 64 4. 96 5. 48 6. 2484 7. 16192 8. 12 9. 240 10. 240