Least Common Multiple (LCM) Worksheets - Free Printable
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Step-by-step solution for: Least Common Multiple (LCM) Worksheets
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Step-by-step solution for: Least Common Multiple (LCM) Worksheets
Absolutely! Let’s solve the worksheet step by step and explain each part clearly.
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## 📌 Part 1: Find the LCM of 3 and 4
We are asked to find the Least Common Multiple (LCM) of 3 and 4.
Multiples of 3 are numbers you get when you multiply 3 by 1, 2, 3, 4, etc.
> The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
Multiples of 4 are numbers you get when you multiply 4 by 1, 2, 3, 4, etc.
> The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Look for numbers that appear in both lists:
- From multiples of 3: 3, 6, 9, 12, 15, 18, 24, ...
- From multiples of 4: 4, 8, 12, 16, 20, 24, ...
> ✔ The common multiples of 3 and 4 are: 12 and 24 (and more like 36, 48, etc.)
The smallest number that appears in both lists is 12.
> ✔ The LCM of 3 and 4 is 12
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## 📌 Part 2: Find the LCM for each pair
We’ll do this one by one using the same method — listing multiples until we find the smallest common one.
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- Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, ...
- Multiples of 7: 7, 14, 21, 28, 35, 42, ...
✔ Common multiples: 14, 28, ...
➡️ LCM = 14
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- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
- Multiples of 10: 10, 20, 30, 40, 50, ...
✔ Common multiples: 20, 40, ...
➡️ LCM = 20
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- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
✔ Common multiples: 20, 40, ...
➡️ LCM = 20
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- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
✔ Common multiples: 30, 60, ...
➡️ LCM = 30
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- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
- Multiples of 12: 12, 24, 36, 48, 60, 72, ...
✔ Common multiples: 24, 48, 72, ...
➡️ LCM = 24
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- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
- Multiples of 18: 18, 36, 54, 72, ...
✔ Common multiples: 18, 36, 54, ...
➡️ LCM = 18
*(Note: Since 18 is a multiple of 6, the LCM is just the larger number, 18.)*
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## ✔ Final Answers:
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, ...
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...
- The common multiples of 3 and 4 are: 12 and 24
- The LCM of 3 and 4 is: 12
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| Pair | LCM |
|------|-----|
| a. 2 and 7 | 14 |
| b. 4 and 10 | 20 |
| c. 4 and 5 | 20 |
| d. 6 and 10 | 30 |
| e. 8 and 12 | 24 |
| f. 6 and 18 | 18 |
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## 💡 Bonus Tip:
You can also find LCM using prime factorization or the formula:
> LCM(a, b) = (a × b) ÷ GCF(a, b)
But for small numbers, listing multiples is the easiest and most visual way — perfect for learning!
---
Let me know if you’d like to see the prime factorization method too! 😊
---
## 📌 Part 1: Find the LCM of 3 and 4
We are asked to find the Least Common Multiple (LCM) of 3 and 4.
Step 1: List the multiples of 3
Multiples of 3 are numbers you get when you multiply 3 by 1, 2, 3, 4, etc.
> The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
Step 2: List the multiples of 4
Multiples of 4 are numbers you get when you multiply 4 by 1, 2, 3, 4, etc.
> The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Step 3: Find the common multiples
Look for numbers that appear in both lists:
- From multiples of 3: 3, 6, 9, 12, 15, 18, 24, ...
- From multiples of 4: 4, 8, 12, 16, 20, 24, ...
> ✔ The common multiples of 3 and 4 are: 12 and 24 (and more like 36, 48, etc.)
Step 4: Find the *least* common multiple
The smallest number that appears in both lists is 12.
> ✔ The LCM of 3 and 4 is 12
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## 📌 Part 2: Find the LCM for each pair
We’ll do this one by one using the same method — listing multiples until we find the smallest common one.
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a. 2 and 7
- Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, ...
- Multiples of 7: 7, 14, 21, 28, 35, 42, ...
✔ Common multiples: 14, 28, ...
➡️ LCM = 14
---
b. 4 and 10
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
- Multiples of 10: 10, 20, 30, 40, 50, ...
✔ Common multiples: 20, 40, ...
➡️ LCM = 20
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c. 4 and 5
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, ...
✔ Common multiples: 20, 40, ...
➡️ LCM = 20
---
d. 6 and 10
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
- Multiples of 10: 10, 20, 30, 40, 50, 60, ...
✔ Common multiples: 30, 60, ...
➡️ LCM = 30
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e. 8 and 12
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
- Multiples of 12: 12, 24, 36, 48, 60, 72, ...
✔ Common multiples: 24, 48, 72, ...
➡️ LCM = 24
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f. 6 and 18
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
- Multiples of 18: 18, 36, 54, 72, ...
✔ Common multiples: 18, 36, 54, ...
➡️ LCM = 18
*(Note: Since 18 is a multiple of 6, the LCM is just the larger number, 18.)*
---
## ✔ Final Answers:
For “Find the LCM of 3 and 4”:
- The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, ...
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...
- The common multiples of 3 and 4 are: 12 and 24
- The LCM of 3 and 4 is: 12
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For “Find the LCM”:
| Pair | LCM |
|------|-----|
| a. 2 and 7 | 14 |
| b. 4 and 10 | 20 |
| c. 4 and 5 | 20 |
| d. 6 and 10 | 30 |
| e. 8 and 12 | 24 |
| f. 6 and 18 | 18 |
---
## 💡 Bonus Tip:
You can also find LCM using prime factorization or the formula:
> LCM(a, b) = (a × b) ÷ GCF(a, b)
But for small numbers, listing multiples is the easiest and most visual way — perfect for learning!
---
Let me know if you’d like to see the prime factorization method too! 😊
Parent Tip: Review the logic above to help your child master the concept of least common denominator worksheet pdf.
