Let's solve each problem on the
GCF/LCM Worksheet by finding the
Least Common Multiple (LCM) of the given pairs of numbers.
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🔷 What is LCM?
The
Least Common Multiple (LCM) of two numbers is the smallest positive number that is divisible by both numbers.
We can find the LCM using:
-
Listing multiples, or
-
Prime factorization method, or
-
Using the formula:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCF}(a, b)}
$$
We'll use a mix of methods for clarity.
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✔ Problem Solutions:
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####
1 a. 4, 2
- Multiples of 4: 4, 8, 12, ...
- Multiples of 2: 2, 4, 6, 8, ...
- Smallest common multiple:
4
✔ LCM = 4
---
####
1 b. 3, 9
- Multiples of 3: 3, 6, 9, 12, ...
- Multiples of 9: 9, 18, 27, ...
- Smallest common multiple:
9
✔ LCM = 9
---
####
2 a. 10, 11
- 10 and 11 are
co-prime (no common factors except 1).
- So, LCM = $10 \times 11 = 110$
✔ LCM = 110
---
####
2 b. 4, 6
- Prime factorization:
- 4 = $2^2$
- 6 = $2 \times 3$
- Take highest powers: $2^2 \times 3 = 4 \times 3 = 12$
✔ LCM = 12
---
####
3 a. 5, 4
- 5 and 4 are co-prime.
- LCM = $5 \times 4 = 20$
✔ LCM = 20
---
####
3 b. 6, 3
- 6 is a multiple of 3 → so LCM is
6
✔ LCM = 6
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####
4 a. 3, 9
- 9 is a multiple of 3 → so LCM is
9
✔ LCM = 9
---
####
4 b. 11, 5
- 11 and 5 are both prime and co-prime.
- LCM = $11 \times 5 = 55$
✔ LCM = 55
---
####
5 a. 12, 8
- Prime factorization:
- 12 = $2^2 \times 3$
- 8 = $2^3$
- Highest powers: $2^3 \times 3 = 8 \times 3 = 24$
✔ LCM = 24
---
####
5 b. 7, 4
- 7 and 4 are co-prime.
- LCM = $7 \times 4 = 28$
✔ LCM = 28
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 a. 4, 2 |
4 |
| 1 b. 3, 9 |
9 |
| 2 a. 10, 11 |
110 |
| 2 b. 4, 6 |
12 |
| 3 a. 5, 4 |
20 |
| 3 b. 6, 3 |
6 |
| 4 a. 3, 9 |
9 |
| 4 b. 11, 5 |
55 |
| 5 a. 12, 8 |
24 |
| 5 b. 7, 4 |
28 |
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📝 Summary Tips:
- If one number is a multiple of the other, the larger number is the LCM.
- For co-prime numbers (no common factors), LCM = product.
- Use prime factorization for larger or tricky numbers.
Let me know if you'd like this worksheet filled out in image format or need explanations for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of lcm and gcf worksheet.
