Let's solve each problem on the
GCF & LCM Sheet 3. We'll find the
Greatest Common Factor (GCF) and the
Least Common Multiple (LCM) for each pair of numbers.
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🔷 Definitions:
-
GCF: The largest number that divides both numbers evenly.
-
LCM: The smallest number that is a multiple of both numbers.
We can use:
-
Prime factorization or
-
Euclidean algorithm for GCF,
- And then use:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCF}(a, b)}
$$
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Let’s go step by step:
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1) 40, 25
Prime factorization:
- 40 = 2³ × 5
- 25 = 5²
GCF: Common prime factors → 5¹ =
5
LCM: Take highest powers: 2³ × 5² = 8 × 25 =
200
✔ GCF =
5, LCM =
200
---
2) 24, 40
Prime factorization:
- 24 = 2³ × 3
- 40 = 2³ × 5
GCF: 2³ =
8
LCM: 2³ × 3 × 5 = 8 × 3 × 5 =
120
✔ GCF =
8, LCM =
120
---
3) 7, 15
- 7 is prime
- 15 = 3 × 5
No common factors → GCF =
1
LCM: 7 × 15 =
105
✔ GCF =
1, LCM =
105
---
4) 32, 16
- 32 = 2⁵
- 16 = 2⁴
GCF: 2⁴ =
16
LCM: 2⁵ =
32
✔ GCF =
16, LCM =
32
---
5) 15, 9
- 15 = 3 × 5
- 9 = 3²
GCF: 3¹ =
3
LCM: 3² × 5 = 9 × 5 =
45
✔ GCF =
3, LCM =
45
---
6) 22, 33
- 22 = 2 × 11
- 33 = 3 × 11
GCF: 11
LCM: 2 × 3 × 11 =
66
✔ GCF =
11, LCM =
66
---
7) 9, 20
- 9 = 3²
- 20 = 2² × 5
No common factors → GCF =
1
LCM: 3² × 2² × 5 = 9 × 4 × 5 =
180
✔ GCF =
1, LCM =
180
---
8) 24, 30
- 24 = 2³ × 3
- 30 = 2 × 3 × 5
GCF: 2 × 3 =
6
LCM: 2³ × 3 × 5 = 8 × 3 × 5 =
120
✔ GCF =
6, LCM =
120
---
9) 11, 15
- 11 is prime
- 15 = 3 × 5
No common factors → GCF =
1
LCM: 11 × 15 =
165
✔ GCF =
1, LCM =
165
---
10) 50, 70
- 50 = 2 × 5²
- 70 = 2 × 5 × 7
GCF: 2 × 5 =
10
LCM: 2 × 5² × 7 = 2 × 25 × 7 =
350
✔ GCF =
10, LCM =
350
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✔ Final Answers:
| Problem | GCF | LCM |
|--------|-----|-----|
| 1) 40, 25 | 5 | 200 |
| 2) 24, 40 | 8 | 120 |
| 3) 7, 15 | 1 | 105 |
| 4) 32, 16 | 16 | 32 |
| 5) 15, 9 | 3 | 45 |
| 6) 22, 33 | 11 | 66 |
| 7) 9, 20 | 1 | 180 |
| 8) 24, 30 | 6 | 120 |
| 9) 11, 15 | 1 | 165 |
| 10) 50, 70 | 10 | 350 |
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Let me know if you'd like this in printable format or with explanations for each!
Parent Tip: Review the logic above to help your child master the concept of finding lcm worksheet.
