Math worksheet for finding the least common denominator of fraction pairs.

Let's solve each problem step by step to find the Least Common Denominator (LCD) for each pair of fractions.

The LCD is the smallest number that both denominators divide into evenly. To find it, we can:

1. List the multiples of each denominator.
2. Find the smallest common multiple.
3. Or use prime factorization and take the highest power of each prime.

We'll go through each one.

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a.) $ \frac{1}{6} $ and $ \frac{2}{3} $

- Denominators: 6 and 3
- Multiples of 6: 6, 12, 18, ...
- Multiples of 3: 3, 6, 9, 12, ...
- Smallest common multiple: 6

✔ LCD = 6

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b.) $ \frac{1}{5} $ and $ \frac{2}{3} $

- Denominators: 5 and 3
- Multiples of 5: 5, 10, 15, 20, ...
- Multiples of 3: 3, 6, 9, 12, 15, ...
- Smallest common multiple: 15

✔ LCD = 15

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c.) $ \frac{1}{4} $ and $ \frac{5}{6} $

- Denominators: 4 and 6
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 6: 6, 12, 18, ...
- Smallest common multiple: 12

✔ LCD = 12

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d.) $ \frac{1}{2} $ and $ \frac{1}{4} $

- Denominators: 2 and 4
- Multiples of 2: 2, 4, 6, 8, ...
- Multiples of 4: 4, 8, 12, ...
- Smallest common multiple: 4

✔ LCD = 4

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e.) $ \frac{5}{8} $ and $ \frac{4}{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, ...
- Smallest common multiple: 72

✔ LCD = 72

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f.) $ \frac{3}{10} $ and $ \frac{1}{5} $

- Denominators: 10 and 5
- Multiples of 10: 10, 20, 30, ...
- Multiples of 5: 5, 10, 15, 20, ...
- Smallest common multiple: 10

✔ LCD = 10

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g.) $ \frac{1}{6} $ and $ \frac{2}{9} $

- Denominators: 6 and 9
- Multiples of 6: 6, 12, 18, 24, ...
- Multiples of 9: 9, 18, 27, ...
- Smallest common multiple: 18

✔ LCD = 18

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h.) $ \frac{7}{8} $ and $ \frac{4}{10} $

- Denominators: 8 and 10
- Multiples of 8: 8, 16, 24, 32, 40, 48, ...
- Multiples of 10: 10, 20, 30, 40, 50, ...
- Smallest common multiple: 40

✔ LCD = 40

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i.) $ \frac{2}{3} $ and $ \frac{1}{8} $

- Denominators: 3 and 8
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
- Multiples of 8: 8, 16, 24, 32, ...
- Smallest common multiple: 24

✔ LCD = 24

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✔ Final Answers:

a. LCD = 6
b. LCD = 15
c. LCD = 12
d. LCD = 4
e. LCD = 72
f. LCD = 10
g. LCD = 18
h. LCD = 40
i. LCD = 24

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Let me know if you'd like help converting these fractions to have the same denominator!