Common Denominators Worksheets - 15 Worksheets Library - Free Printable

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 in each pair. Here's how to approach each part:

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Step-by-Step Solution:

#### a) \( \frac{1}{6} \) and \( \frac{2}{3} \)
- Denominators: 6 and 3
- Find the least common multiple (LCM) of 6 and 3:
- Multiples of 6: 6, 12, 18, ...
- Multiples of 3: 3, 6, 9, 12, ...
- The smallest common multiple is 6.
- LCD = 6

#### b) \( \frac{1}{4} \) and \( \frac{5}{6} \)
- Denominators: 4 and 6
- Find the LCM of 4 and 6:
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 6: 6, 12, 18, ...
- The smallest common multiple is 12.
- LCD = 12

#### c) \( \frac{5}{8} \) and \( \frac{4}{9} \)
- Denominators: 8 and 9
- Find the LCM of 8 and 9:
- Multiples of 8: 8, 16, 24, 32, 72, ...
- Multiples of 9: 9, 18, 27, 36, 72, ...
- The smallest common multiple is 72.
- LCD = 72

#### d) \( \frac{1}{6} \) and \( \frac{2}{9} \)
- Denominators: 6 and 9
- Find the LCM of 6 and 9:
- Multiples of 6: 6, 12, 18, 24, ...
- Multiples of 9: 9, 18, 27, ...
- The smallest common multiple is 18.
- LCD = 18

#### e) \( \frac{2}{3} \) and \( \frac{1}{8} \)
- Denominators: 3 and 8
- Find the LCM of 3 and 8:
- Multiples of 3: 3, 6, 9, 12, 24, ...
- Multiples of 8: 8, 16, 24, ...
- The smallest common multiple is 24.
- LCD = 24

#### f) \( \frac{5}{6} \) and \( \frac{2}{3} \)
- Denominators: 6 and 3
- Find the LCM of 6 and 3:
- Multiples of 6: 6, 12, 18, ...
- Multiples of 3: 3, 6, 9, 12, ...
- The smallest common multiple is 6.
- LCD = 6

#### g) \( \frac{1}{5} \) and \( \frac{2}{3} \)
- Denominators: 5 and 3
- Find the LCM of 5 and 3:
- Multiples of 5: 5, 10, 15, 20, ...
- Multiples of 3: 3, 6, 9, 15, ...
- The smallest common multiple is 15.
- LCD = 15

#### h) \( \frac{1}{2} \) and \( \frac{1}{4} \)
- Denominators: 2 and 4
- Find the LCM of 2 and 4:
- Multiples of 2: 2, 4, 6, 8, ...
- Multiples of 4: 4, 8, 12, ...
- The smallest common multiple is 4.
- LCD = 4

#### i) \( \frac{3}{10} \) and \( \frac{1}{5} \)
- Denominators: 10 and 5
- Find the LCM of 10 and 5:
- Multiples of 10: 10, 20, 30, ...
- Multiples of 5: 5, 10, 15, ...
- The smallest common multiple is 10.
- LCD = 10

#### j) \( \frac{7}{8} \) and \( \frac{4}{10} \)
- Denominators: 8 and 10
- Find the LCM of 8 and 10:
- Multiples of 8: 8, 16, 24, 40, ...
- Multiples of 10: 10, 20, 30, 40, ...
- The smallest common multiple is 40.
- LCD = 40

#### k) \( \frac{1}{6} \) and \( \frac{2}{4} \)
- Denominators: 6 and 4
- Find the LCM of 6 and 4:
- Multiples of 6: 6, 12, 18, ...
- Multiples of 4: 4, 8, 12, 16, ...
- The smallest common multiple is 12.
- LCD = 12

#### l) \( \frac{8}{9} \) and \( \frac{2}{3} \)
- Denominators: 9 and 3
- Find the LCM of 9 and 3:
- Multiples of 9: 9, 18, 27, ...
- Multiples of 3: 3, 6, 9, 12, ...
- The smallest common multiple is 9.
- LCD = 9

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{a) } 6 & \text{g) } 15 \\
\text{b) } 12 & \text{h) } 4 \\
\text{c) } 72 & \text{i) } 10 \\
\text{d) } 18 & \text{j) } 40 \\
\text{e) } 24 & \text{k) } 12 \\
\text{f) } 6 & \text{l) } 9 \\
\end{array}
}
\]

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This completes the solution. Each LCD is determined by finding the smallest number that is a multiple of both denominators in the given pairs.