Sure! Let’s solve each problem on the
GCF & LCM Sheet 3 by finding the
Greatest Common Factor (GCF) and the
Least Common Multiple (LCM) for each pair of numbers.
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📌 Key Concepts:
-
GCF (Greatest Common Factor): The largest number that divides both numbers evenly.
-
LCM (Least Common Multiple): The smallest number that is a multiple of both numbers.
We can find them using:
-
Prime factorization
- Or listing factors/multiples (for smaller numbers)
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##
✔ Problem-by-Problem Solutions:
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1) 40, 25
-
Prime factors:
- 40 = 2 × 2 × 2 × 5
- 25 = 5 × 5
-
GCF: Only common prime factor is
5 →
GCF = 5
-
LCM: Take highest powers of all primes: 2³ × 5² = 8 × 25 =
200
✔ Answer: GCF = 5, LCM = 200
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2) 24, 40
-
Prime factors:
- 24 = 2 × 2 × 2 × 3
- 40 = 2 × 2 × 2 × 5
-
GCF: Common primes: 2³ →
GCF = 8
-
LCM: 2³ × 3 × 5 = 8 × 3 × 5 =
120
✔ Answer: GCF = 8, LCM = 120
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3) 7, 15
- 7 is prime, 15 = 3 × 5 → no common factors except 1
-
GCF = 1
-
LCM: Since coprime, LCM = 7 × 15 =
105
✔ Answer: GCF = 1, LCM = 105
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4) 32, 16
- 32 = 2⁵, 16 = 2⁴
-
GCF: 2⁴ =
16
-
LCM: 2⁵ =
32
✔ Answer: GCF = 16, LCM = 32
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5) 15, 9
- 15 = 3 × 5, 9 = 3²
-
GCF: 3
-
LCM: 3² × 5 = 9 × 5 =
45
✔ Answer: GCF = 3, LCM = 45
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6) 22, 33
- 22 = 2 × 11, 33 = 3 × 11
-
GCF: 11
-
LCM: 2 × 3 × 11 =
66
✔ Answer: GCF = 11, LCM = 66
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7) 9, 20
- 9 = 3², 20 = 2² × 5 → no common factors
-
GCF = 1
-
LCM = 9 × 20 = 180
✔ Answer: GCF = 1, LCM = 180
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8) 24, 30
- 24 = 2³ × 3, 30 = 2 × 3 × 5
-
GCF: 2 × 3 =
6
-
LCM: 2³ × 3 × 5 = 8 × 3 × 5 =
120
✔ Answer: GCF = 6, LCM = 120
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9) 11, 15
- 11 is prime, 15 = 3 × 5 → no common factors
-
GCF = 1
-
LCM = 11 × 15 = 165
✔ Answer: GCF = 1, LCM = 165
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10) 50, 70
- 50 = 2 × 5², 70 = 2 × 5 × 7
-
GCF: 2 × 5 =
10
-
LCM: 2 × 5² × 7 = 2 × 25 × 7 =
350
✔ Answer: GCF = 10, LCM = 350
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## 🧾 Final Answer Table:
| # | Numbers | 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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You can now fill in your worksheet with these answers!
Let me know if you’d like to see step-by-step factor trees or another method. 😊
Parent Tip: Review the logic above to help your child master the concept of lcm worksheet with answers.
