Let’s solve each problem step by step. We’re looking for the
Least Common Denominator (LCD) — that means the smallest number that both denominators can divide into evenly.
We’ll go one pair at a time.
---
a. 1/6 and 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
---
b. 1/5 and 2/3
Denominators: 5 and 3
They have no common factors except 1 → multiply them: 5 × 3 =
15
→ LCD =
15
---
c. 1/4 and 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
---
d. 1/2 and 1/4
Denominators: 2 and 4
4 is a multiple of 2 → so LCD =
4
→ LCD =
4
---
e. 5/8 and 4/9
Denominators: 8 and 9
No common factors → multiply: 8 × 9 =
72
→ LCD =
72
---
f. 3/10 and 1/5
Denominators: 10 and 5
10 is a multiple of 5 → LCD =
10
→ LCD =
10
---
g. 1/6 and 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
---
h. 7/8 and 4/10
First, simplify 4/10 → it becomes 2/5 (but we don’t need to simplify to find LCD — just use original denominators: 8 and 10)
Denominators: 8 and 10
Multiples of 8: 8, 16, 24, 32, 40…
Multiples of 10: 10, 20, 30, 40…
Smallest common multiple =
40
→ LCD =
40
*(Note: Even if you simplified 4/10 to 2/5, denominators would be 8 and 5 → LCD = 40 still! So same answer.)*
---
i. 2/3 and 1/8
Denominators: 3 and 8
No common factors → multiply: 3 × 8 =
24
→ LCD =
24
---
Final Answer:
a. 6
b. 15
c. 12
d. 4
e. 72
f. 10
g. 18
h. 40
i. 24
Parent Tip: Review the logic above to help your child master the concept of least common denominator worksheet pdf.
