Explanation:
We need to find the
Least Common Denominator (LCD) for each pair of fractions. The LCD is the smallest number that both denominators divide into evenly — in other words, the
Least Common Multiple (LCM) of the two denominators.
Let’s go one pair at a time:
---
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
---
b. $\frac{1}{5}$ and $\frac{2}{3}$
Denominators: 5 and 3
5 is prime, 3 is prime → LCM = $5 \times 3 = 15$
✔ LCD =
15
---
c. $\frac{1}{4}$ and $\frac{5}{6}$
Denominators: 4 and 6
Prime factors:
- 4 = $2^2$
- 6 = $2 \times 3$
LCM = highest powers: $2^2 \times 3 = 4 \times 3 = 12$
✔ LCD =
12
---
d. $\frac{1}{2}$ and $\frac{1}{4}$
Denominators: 2 and 4
Multiples of 2: 2, 4, 6, ...
Multiples of 4: 4, 8, ...
→ Smallest common =
4
✔ LCD =
4
---
e. $\frac{5}{8}$ and $\frac{4}{9}$
Denominators: 8 and 9
8 = $2^3$, 9 = $3^2$ → no common factors
LCM = $8 \times 9 = 72$
✔ LCD =
72
---
f. $\frac{3}{10}$ and $\frac{1}{5}$
Denominators: 10 and 5
10 is a multiple of 5 → LCM =
10
✔ LCD =
10
---
g. $\frac{1}{6}$ 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
---
h. $\frac{7}{8}$ 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
---
i. $\frac{2}{3}$ and $\frac{1}{8}$
Denominators: 3 and 8
3 is prime, 8 = $2^3$ → no common factors
LCM = $3 \times 8 = 24$
✔ LCD =
24
Now double-check all:
a. 6 ✔
b. 15 ✔
c. 12 ✔
d. 4 ✔
e. 72 ✔
f. 10 ✔
g. 18 ✔
h. 40 ✔
i. 24 ✔
All correct.
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 finding the least common denominator worksheet.
