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
GCF:
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 25: 1, 5, 25
→ Common factors: 1, 5 → GCF =
5
LCM:
Multiples of 40: 40, 80, 120, 160, 200...
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200...
→ First common multiple:
200
✔ GCF = 5, LCM = 200
---
2) 24, 40
GCF:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
→ Common: 1, 2, 4, 8 → GCF =
8
LCM:
Multiples of 24: 24, 48, 72, 96, 120...
Multiples of 40: 40, 80, 120...
→ First common:
120
✔ GCF = 8, LCM = 120
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3) 7, 15
GCF:
7 is prime → factors: 1, 7
15: 1, 3, 5, 15
→ Only common factor:
1
LCM: Since they’re coprime (no common factors except 1), LCM = 7 × 15 =
105
✔ GCF = 1, LCM = 105
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4) 32, 16
GCF:
16 divides 32 evenly → GCF =
16
LCM: Since 32 is a multiple of 16, LCM =
32
✔ GCF = 16, LCM = 32
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5) 15, 9
GCF:
15: 1, 3, 5, 15
9: 1, 3, 9
→ Common: 1, 3 → GCF =
3
LCM:
Multiples of 15: 15, 30, 45...
Multiples of 9: 9, 18, 27, 36, 45...
→ First common:
45
✔ GCF = 3, LCM = 45
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6) 22, 33
GCF:
22: 1, 2, 11, 22
33: 1, 3, 11, 33
→ Common: 1, 11 → GCF =
11
LCM:
Use formula: LCM = (a × b) / GCF = (22 × 33) / 11 = 726 / 11 =
66
Check: Multiples of 22: 22, 44, 66...
Multiples of 33: 33, 66... → Yes, 66
✔ GCF = 11, LCM = 66
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7) 9, 20
GCF:
9: 1, 3, 9
20: 1, 2, 4, 5, 10, 20
→ Only common:
1
LCM: 9 × 20 =
180 (since no common factors)
✔ GCF = 1, LCM = 180
---
8) 24, 30
GCF:
24: 1, 2, 3, 4, 6, 8, 12, 24
30: 1, 2, 3, 5, 6, 10, 15, 30
→ Common: 1, 2, 3, 6 → GCF =
6
LCM: (24 × 30) / 6 = 720 / 6 =
120
Check: Multiples of 24: 24, 48, 72, 96, 120...
Multiples of 30: 30, 60, 90, 120... → Yes
✔ GCF = 6, LCM = 120
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9) 11, 15
GCF:
11 is prime → 1, 11
15: 1, 3, 5, 15
→ Only common:
1
LCM: 11 × 15 =
165
✔ GCF = 1, LCM = 165
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10) 50, 70
GCF:
50: 1, 2, 5, 10, 25, 50
70: 1, 2, 5, 7, 10, 14, 35, 70
→ Common: 1, 2, 5, 10 → GCF =
10
LCM: (50 × 70) / 10 = 3500 / 10 =
350
Check: Multiples of 50: 50, 100, 150, 200, 250, 300, 350...
Multiples of 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 gcf and lcm worksheet with answers.
