GCF and LCM - Free Printable

$GCF and LCM$

Educational worksheet: GCF and LCM. Download and print for classroom or home learning activities.

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Show Answer Key & Explanations Step-by-step solution for: GCF and LCM

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Let’s solve each problem step by step. We’ll find the GCF (Greatest Common Factor) and LCM (Least Common Multiple) for each pair of numbers.

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1) 40, 25

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 25: 1, 5, 25
→ GCF = 5

Multiples of 40: 40, 80, 120, 160, 200...
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200...
→ LCM = 200

✔ GCF: 5, LCM: 200

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2) 24, 40

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
→ GCF = 8

Use formula: LCM = (24 × 40) ÷ GCF = 960 ÷ 8 = 120
Or list multiples:
24 → 24, 48, 72, 96, 120...
40 → 40, 80, 120...
→ LCM = 120

✔ 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 = 7 × 15 = 105 (since they’re coprime)

✔ GCF: 1, LCM: 105

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4) 32, 16

16 divides into 32 evenly → GCF = 16
LCM = 32 (since 32 is a multiple of 16)

✔ GCF: 16, LCM: 32

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5) 15, 9

Factors of 15: 1, 3, 5, 15
Factors of 9: 1, 3, 9
→ GCF = 3

LCM = (15 × 9) ÷ 3 = 135 ÷ 3 = 45
Check: Multiples of 15: 15, 30, 45...; 9: 9, 18, 27, 36, 45 → yes!

✔ GCF: 3, LCM: 45

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6) 22, 33

22 = 2×11, 33 = 3×11 → common factor is 11
→ GCF = 11

LCM = (22 × 33) ÷ 11 = 726 ÷ 11 = 66
Check: 22 → 22, 44, 66; 33 → 33, 66 → yes!

✔ 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

✔ GCF: 1, LCM: 180

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8) 24, 30

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
→ GCF = 6

LCM = (24 × 30) ÷ 6 = 720 ÷ 6 = 120
Check: 24 → 24, 48, 72, 96, 120; 30 → 30, 60, 90, 120 → yes!

✔ 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

✔ GCF: 1, LCM: 165

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10) 50, 70

50 = 2×5², 70 = 2×5×7 → common: 2×5 = 10
→ GCF = 10

LCM = (50 × 70) ÷ 10 = 3500 ÷ 10 = 350
Check: 50 → 50, 100, 150, 200, 250, 300, 350; 70 → 70, 140, 210, 280, 350 → yes!

✔ GCF: 10, LCM: 350

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Final Answer:
1) GCF: 5, LCM: 200
2) GCF: 8, LCM: 120
3) GCF: 1, LCM: 105
4) GCF: 16, LCM: 32
5) GCF: 3, LCM: 45
6) GCF: 11, LCM: 66
7) GCF: 1, LCM: 180
8) GCF: 6, LCM: 120
9) GCF: 1, LCM: 165
10) GCF: 10, LCM: 350

Parent Tip: Review the logic above to help your child master the concept of math gcf worksheet pdf.

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