Let's solve each of the four problems to find the
Least Common Denominator (LCD) for the given pairs of fractions.
---
🔹 Problem 1: Find the LCD of
$$
\frac{3}{10} \text{ and } \frac{5}{6}
$$
Step 1: List the multiples of each denominator:
- Multiples of 10: 10, 20, 30, 40, 50, ...
- Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Step 2: Find the smallest common multiple.
- The first common multiple is
30.
✔ LCD = 30
---
🔹 Problem 2: Find the LCD of
$$
\frac{2}{3} \text{ and } \frac{1}{7}
$$
Step 1: List the multiples:
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
- Multiples of 7: 7, 14, 21, 28, ...
Step 2: Smallest common multiple is
21.
✔ LCD = 21
---
🔹 Problem 3: Find the LCD of
$$
\frac{5}{8} \text{ and } \frac{4}{7}
$$
Step 1: Multiples:
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
- Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, ...
Step 2: First common multiple is
56.
✔ LCD = 56
---
🔹 Problem 4: Find the LCD of
$$
\frac{1}{4} \text{ and } \frac{3}{8}
$$
Step 1: Multiples:
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 8: 8, 16, 24, ...
Step 2: Smallest common multiple is
8.
✔ LCD = 8
---
✔ Final Answers:
1.
LCD = 30
2.
LCD = 21
3.
LCD = 56
4.
LCD = 8
---
💡
Tip: You can also find the LCD by using the
LCM (Least Common Multiple) of the denominators. This is especially helpful when numbers are larger.
Let me know if you'd like a step-by-step method using prime factorization!
Parent Tip: Review the logic above to help your child master the concept of finding the least common denominator fractions worksheet.
