Sure! Let’s solve each problem step by step. The goal is to find the
Least Common Denominator (LCD) for each pair of fractions. The LCD is the
Least Common Multiple (LCM) of the denominators.
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🔢 Step-by-step Solutions:
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a. 1/6 and 2/3
- Denominators: 6 and 3
- LCM of 6 and 3:
- Multiples of 3: 3, 6, 9, 12...
- Multiples of 6: 6, 12, 18...
- Smallest common multiple:
6
✔ LCD = 6
---
b. 1/5 and 2/3
- Denominators: 5 and 3
- 5 and 3 are both prime → LCM = 5 × 3 =
15
✔ LCD = 15
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c. 1/4 and 5/6
- Denominators: 4 and 6
- Prime factorization:
- 4 = 2²
- 6 = 2 × 3
- LCM = highest powers: 2² × 3 = 4 × 3 =
12
✔ LCD = 12
---
d. 1/2 and 1/4
- Denominators: 2 and 4
- 4 is a multiple of 2 → LCM =
4
✔ LCD = 4
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e. 5/8 and 4/9
- Denominators: 8 and 9
- 8 = 2³, 9 = 3² → no common factors → LCM = 8 × 9 =
72
✔ LCD = 72
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f. 3/10 and 1/5
- Denominators: 10 and 5
- 10 is a multiple of 5 → LCM =
10
✔ LCD = 10
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g. 1/6 and 2/9
- Denominators: 6 and 9
- Prime factors:
- 6 = 2 × 3
- 9 = 3²
- LCM = 2 × 3² = 2 × 9 =
18
✔ LCD = 18
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h. 7/8 and 4/10
- Denominators: 8 and 10
- Prime factors:
- 8 = 2³
- 10 = 2 × 5
- LCM = 2³ × 5 = 8 × 5 =
40
✔ LCD = 40
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i. 2/3 and 1/8
- Denominators: 3 and 8
- 3 is prime, 8 = 2³ → no common factors → LCM = 3 × 8 =
24
✔ LCD = 24
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##
✔ Final Answers:
| Problem | LCD |
|---------|-----|
| a. | 6 |
| b. | 15 |
| c. | 12 |
| d. | 4 |
| e. | 72 |
| f. | 10 |
| g. | 18 |
| h. | 40 |
| i. | 24 |
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## 💡 Quick Tip:
To find LCD:
1. List the denominators.
2. Find LCM using prime factorization or listing multiples.
3. If one denominator divides the other, the larger one is the LCD.
4. If denominators are coprime (no common factors), multiply them.
Let me know if you want to see how to rewrite the fractions using these LCDs! 😊
Parent Tip: Review the logic above to help your child master the concept of finding common denominators worksheet.
