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.

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🔷 What is the LCD?

The Least Common Denominator is the least common multiple (LCM) of the denominators of two or more fractions. It allows you to rewrite fractions with the same denominator so they can be added, subtracted, or compared.

We'll find the LCM of the denominators in each pair.

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✔ Step-by-step Solutions:

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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...
- LCM = 6

✔ LCD = 6

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#### b) $ \frac{1}{4} $ and $ \frac{5}{6} $

- Denominators: 4 and 6
- Multiples of 4: 4, 8, 12, 16...
- Multiples of 6: 6, 12, 18...
- LCM = 12

✔ LCD = 12

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#### c) $ \frac{5}{8} $ and $ \frac{4}{9} $

- Denominators: 8 and 9
- 8 = $ 2^3 $
- 9 = $ 3^2 $
- LCM = $ 2^3 \times 3^2 = 8 \times 9 = 72 $

✔ LCD = 72

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#### d) $ \frac{1}{6} $ and $ \frac{2}{9} $

- Denominators: 6 and 9
- 6 = $ 2 \times 3 $
- 9 = $ 3^2 $
- LCM = $ 2 \times 3^2 = 2 \times 9 = 18 $

✔ LCD = 18

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#### e) $ \frac{2}{5} $ and $ \frac{1}{8} $

- Denominators: 5 and 8
- 5 is prime, 8 = $ 2^3 $
- LCM = $ 5 \times 8 = 40 $

✔ LCD = 40

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#### f) $ \frac{5}{6} $ and $ \frac{2}{3} $

- Denominators: 6 and 3
- 6 is divisible by 3 → LCM = 6

✔ LCD = 6

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#### g) $ \frac{1}{5} $ and $ \frac{2}{3} $

- Denominators: 5 and 3
- Both are prime → LCM = $ 5 \times 3 = 15 $

✔ LCD = 15

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#### h) $ \frac{1}{2} $ and $ \frac{1}{4} $

- Denominators: 2 and 4
- 4 is divisible by 2 → LCM = 4

✔ LCD = 4

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#### i) $ \frac{3}{10} $ and $ \frac{1}{5} $

- Denominators: 10 and 5
- 10 is divisible by 5 → LCM = 10

✔ LCD = 10

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#### j) $ \frac{7}{8} $ and $ \frac{4}{10} $

- Denominators: 8 and 10
- 8 = $ 2^3 $
- 10 = $ 2 \times 5 $
- LCM = $ 2^3 \times 5 = 8 \times 5 = 40 $

✔ LCD = 40

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#### k) $ \frac{1}{6} $ and $ \frac{2}{4} $

- Simplify $ \frac{2}{4} = \frac{1}{2} $, but we still use original denominators.
- Denominators: 6 and 4
- 6 = $ 2 \times 3 $
- 4 = $ 2^2 $
- LCM = $ 2^2 \times 3 = 4 \times 3 = 12 $

✔ LCD = 12

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#### l) $ \frac{8}{9} $ and $ \frac{2}{3} $

- Denominators: 9 and 3
- 9 is divisible by 3 → LCM = 9

✔ LCD = 9

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✔ Final Answers:

| Problem | LCD |
|--------|-----|
| a) | 6 |
| b) | 12 |
| c) | 72 |
| d) | 18 |
| e) | 40 |
| f) | 6 |
| g) | 15 |
| h) | 4 |
| i) | 10 |
| j) | 40 |
| k) | 12 |
| l) | 9 |

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🎉 How Did You Do?

You can now fill in the blanks on the worksheet!

> Answer Key:
> a) 6
> b) 12
> c) 72
> d) 18
> e) 40
> f) 6
> g) 15
> h) 4
> i) 10
> j) 40
> k) 12
> l) 9

And don't forget to smile! 😊😊😊

Let me know if you'd like help converting these fractions to equivalent forms using the LCD!