Comprehensive worksheet designed for 5th graders to practice calculating the least common denominator for various fraction pairs.

To solve the problem of finding the least common denominator (LCD) for each pair of fractions, we need to determine the smallest number that is a multiple of both denominators. Here's how to approach each problem step by step:

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General Steps to Find the LCD:

1. Identify the denominators of the two fractions.
2. Find the Least Common Multiple (LCM) of the two denominators. The LCM is the smallest number that is divisible by both denominators.
3. The LCM of the denominators is the LCD.

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Solutions for Each Problem:

#### Problem 1: \( \frac{1}{3} \) and \( \frac{5}{6} \)
- Denominators: 3 and 6
- Multiples of 3: 3, 6, 9, 12, ...
- Multiples of 6: 6, 12, 18, ...
- LCM of 3 and 6: 6
- LCD: 6

#### Problem 2: \( \frac{3}{4} \) and \( \frac{1}{8} \)
- Denominators: 4 and 8
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 8: 8, 16, 24, ...
- LCM of 4 and 8: 8
- LCD: 8

#### Problem 3: \( \frac{5}{6} \) and \( \frac{5}{12} \)
- Denominators: 6 and 12
- Multiples of 6: 6, 12, 18, ...
- Multiples of 12: 12, 24, 36, ...
- LCM of 6 and 12: 12
- LCD: 12

#### Problem 4: \( \frac{3}{8} \) and \( \frac{19}{24} \)
- Denominators: 8 and 24
- Multiples of 8: 8, 16, 24, 32, ...
- Multiples of 24: 24, 48, 72, ...
- LCM of 8 and 24: 24
- LCD: 24

#### Problem 5: \( \frac{4}{5} \) and \( \frac{13}{15} \)
- Denominators: 5 and 15
- Multiples of 5: 5, 10, 15, 20, ...
- Multiples of 15: 15, 30, 45, ...
- LCM of 5 and 15: 15
- LCD: 15

#### Problem 6: \( \frac{7}{12} \) and \( \frac{1}{2} \)
- Denominators: 12 and 2
- Multiples of 12: 12, 24, 36, ...
- Multiples of 2: 2, 4, 6, 8, 10, 12, ...
- LCM of 12 and 2: 12
- LCD: 12

#### Problem 7: \( \frac{3}{8} \) and \( \frac{2}{5} \)
- Denominators: 8 and 5
- Multiples of 8: 8, 16, 24, 32, 40, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
- LCM of 8 and 5: 40
- LCD: 40

#### Problem 8: \( \frac{4}{9} \) and \( \frac{7}{11} \)
- Denominators: 9 and 11
- Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ...
- Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, ...
- LCM of 9 and 11: 99
- LCD: 99

#### Problem 9: \( \frac{6}{7} \) and \( \frac{2}{5} \)
- Denominators: 7 and 5
- Multiples of 7: 7, 14, 21, 28, 35, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, ...
- LCM of 7 and 5: 35
- LCD: 35

#### Problem 10: \( \frac{3}{5} \) and \( \frac{1}{4} \)
- Denominators: 5 and 4
- Multiples of 5: 5, 10, 15, 20, 25, ...
- Multiples of 4: 4, 8, 12, 16, 20, 24, ...
- LCM of 5 and 4: 20
- LCD: 20

#### Problem 11: \( \frac{2}{9} \) and \( \frac{5}{6} \)
- Denominators: 9 and 6
- Multiples of 9: 9, 18, 27, 36, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...
- LCM of 9 and 6: 18
- LCD: 18

#### Problem 12: \( \frac{3}{4} \) and \( \frac{1}{6} \)
- Denominators: 4 and 6
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 6: 6, 12, 18, 24, ...
- LCM of 4 and 6: 12
- LCD: 12

#### Problem 13: \( \frac{7}{8} \) and \( \frac{5}{12} \)
- Denominators: 8 and 12
- Multiples of 8: 8, 16, 24, 32, ...
- Multiples of 12: 12, 24, 36, ...
- LCM of 8 and 12: 24
- LCD: 24

#### Problem 14: \( \frac{1}{18} \) and \( \frac{1}{27} \)
- Denominators: 18 and 27
- Multiples of 18: 18, 36, 54, 72, ...
- Multiples of 27: 27, 54, 81, ...
- LCM of 18 and 27: 54
- LCD: 54

#### Problem 15: \( \frac{3}{25} \) and \( \frac{7}{30} \)
- Denominators: 25 and 30
- Multiples of 25: 25, 50, 75, 100, 125, 150, ...
- Multiples of 30: 30, 60, 90, 120, 150, ...
- LCM of 25 and 30: 150
- LCD: 150

#### Problem 16: \( \frac{25}{28} \) and \( \frac{20}{21} \)
- Denominators: 28 and 21
- Multiples of 28: 28, 56, 84, 112, ...
- Multiples of 21: 21, 42, 63, 84, ...
- LCM of 28 and 21: 84
- LCD: 84

#### Problem 17: \( \frac{4}{45} \) and \( \frac{11}{72} \)
- Denominators: 45 and 72
- Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, ...
- Multiples of 72: 72, 144, 216, 288, 360, ...
- LCM of 45 and 72: 360
- LCD: 360

#### Problem 18: \( \frac{1}{8} \) and \( \frac{1}{9} \)
- Denominators: 8 and 9
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
- Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, ...
- LCM of 8 and 9: 72
- LCD: 72

#### Problem 19: \( \frac{8}{15} \) and \( \frac{9}{25} \)
- Denominators: 15 and 25
- Multiples of 15: 15, 30, 45, 60, 75, 90, ...
- Multiples of 25: 25, 50, 75, 100, ...
- LCM of 15 and 25: 75
- LCD: 75

#### Problem 20: \( \frac{1}{20} \) and \( \frac{5}{24} \)
- Denominators: 20 and 24
- Multiples of 20: 20, 40, 60, 80, 100, 120, ...
- Multiples of 24: 24, 48, 72, 96, 120, ...
- LCM of 20 and 24: 120
- LCD: 120

#### Problem 21: \( \frac{35}{36} \) and \( \frac{1}{60} \)
- Denominators: 36 and 60
- Multiples of 36: 36, 72, 108, 144, 180, 216, ...
- Multiples of 60: 60, 120, 180, 240, ...
- LCM of 36 and 60: 180
- LCD: 180

#### Problem 22: \( \frac{3}{16} \) and \( \frac{5}{56} \)
- Denominators: 16 and 56
- Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, ...
- Multiples of 56: 56, 112, 168, ...
- LCM of 16 and 56: 112
- LCD: 112

#### Problem 23: \( \frac{19}{24} \) and \( \frac{7}{36} \)
- Denominators: 24 and 36
- Multiples of 24: 24, 48, 72, 96, ...
- Multiples of 36: 36, 72, 108, ...
- LCM of 24 and 36: 72
- LCD: 72

#### Problem 24: \( \frac{21}{45} \) and \( \frac{17}{27} \)
- Denominators: 45 and 27
- Multiples of 45: 45, 90, 135, 180, ...
- Multiples of 27: 27, 54, 81, 108, 135, ...
- LCM of 45 and 27: 135
- LCD: 135

#### Problem 25: \( \frac{13}{48} \) and \( \frac{7}{20} \)
- Denominators: 48 and 20
- Multiples of 48: 48, 96, 144, 192, 240, ...
- Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, ...
- LCM of 48 and 20: 240
- LCD: 240

#### Problem 26: \( \frac{3}{16} \) and \( \frac{17}{24} \)
- Denominators: 16 and 24
- Multiples of 16: 16, 32, 48, 64, 80, ...
- Multiples of 24: 24, 48, 72, 96, ...
- LCM of 16 and 24: 48
- LCD: 48

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & 6 \\
2. & 8 \\
3. & 12 \\
4. & 24 \\
5. & 15 \\
6. & 12 \\
7. & 40 \\
8. & 99 \\
9. & 35 \\
10. & 20 \\
11. & 18 \\
12. & 12 \\
13. & 24 \\
14. & 54 \\
15. & 150 \\
16. & 84 \\
17. & 360 \\
18. & 72 \\
19. & 75 \\
20. & 120 \\
21. & 180 \\
22. & 112 \\
23. & 72 \\
24. & 135 \\
25. & 240 \\
26. & 48 \\
\end{array}
}
\]