Common Denominators Worksheets - 15 Worksheets Library - Free Printable

Sure! Let’s solve the “Least Common Denominators” worksheet step by step.

---

📌 What is a Least Common Denominator (LCD)?

The Least Common Denominator of two fractions is the smallest number that both denominators can divide into evenly. It’s the same as the Least Common Multiple (LCM) of the two denominators.

To find it:
1. List the multiples of each denominator.
2. Find the smallest multiple they have in common.

Alternatively, you can use prime factorization or the formula:

> LCM(a, b) = (a × b) / GCF(a, b)

But for small numbers (like on this worksheet), listing multiples is easiest.

---

Let’s solve each pair:

---

✔ a) 1/6 and 2/3

Denominators: 6 and 3
Multiples of 6: 6, 12, 18...
Multiples of 3: 3, 6, 9, 12...
→ LCD = 6

---

✔ b) 1/4 and 5/6

Denominators: 4 and 6
Multiples of 4: 4, 8, 12, 16...
Multiples of 6: 6, 12, 18...
→ LCD = 12

---

✔ c) 5/8 and 4/9

Denominators: 8 and 9
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72...
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72...
→ LCD = 72

*(Note: 8 and 9 are coprime — no common factors — so LCM = 8×9 = 72)*

---

✔ d) 1/6 and 2/9

Denominators: 6 and 9
Multiples of 6: 6, 12, 18, 24...
Multiples of 9: 9, 18, 27...
→ LCD = 18

---

✔ e) 2/3 and 1/8

Denominators: 3 and 8
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...
Multiples of 8: 8, 16, 24, 32...
→ LCD = 24

---

✔ f) 5/6 and 2/3

Denominators: 6 and 3
Multiples of 6: 6, 12, 18...
Multiples of 3: 3, 6, 9...
→ LCD = 6

---

✔ g) 1/5 and 2/3

Denominators: 5 and 3
Multiples of 5: 5, 10, 15, 20...
Multiples of 3: 3, 6, 9, 12, 15...
→ LCD = 15

---

✔ h) 1/2 and 1/4

Denominators: 2 and 4
Multiples of 2: 2, 4, 6...
Multiples of 4: 4, 8, 12...
→ LCD = 4

---

✔ i) 3/10 and 1/5

Denominators: 10 and 5
Multiples of 10: 10, 20...
Multiples of 5: 5, 10, 15...
→ LCD = 10

---

✔ j) 7/8 and 4/10

Denominators: 8 and 10
Multiples of 8: 8, 16, 24, 32, 40...
Multiples of 10: 10, 20, 30, 40...
→ LCD = 40

---

✔ k) 1/6 and 2/4

Denominators: 6 and 4
Multiples of 6: 6, 12, 18...
Multiples of 4: 4, 8, 12, 16...
→ LCD = 12

*(Note: 2/4 simplifies to 1/2, but we still use original denominator 4 unless told to simplify first.)*

---

✔ l) 8/9 and 2/3

Denominators: 9 and 3
Multiples of 9: 9, 18...
Multiples of 3: 3, 6, 9, 12...
→ LCD = 9

---

## ✔ Final Answers:

| Problem | LCD |
|---------|-----|
| a) | 6 |
| b) | 12 |
| c) | 72 |
| d) | 18 |
| e) | 24 |
| f) | 6 |
| g) | 15 |
| h) | 4 |
| i) | 10 |
| j) | 40 |
| k) | 12 |
| l) | 9 |

---

## 💡 How Did You Do?

You can check your answers against the table above. If you got all 12 correct — 👏 Great job!
If you made a few mistakes — don’t worry! Practice makes perfect. Try re-doing the ones you missed using the multiples method.

---

✔ Tip: Always write down the multiples — it helps avoid mistakes!

Let me know if you want to see how to rewrite the fractions with these LCDs too! 😊