Sure! Let’s solve each pair for
LCM (Least Common Multiple) and
GCF (Greatest Common Factor) step by step.
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🔢 Definitions:
-
GCF = Largest number that divides both numbers evenly.
-
LCM = Smallest number that both numbers divide into evenly.
We can use
prime factorization or
listing multiples/factors. I’ll use prime factorization for accuracy.
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## 1.
16, 10
- Prime factors:
- 16 = 2⁴
- 10 = 2 × 5
-
GCF = common prime factors with lowest exponent → only
2¹ = 2
-
LCM = all prime factors with highest exponent → 2⁴ × 5 = 16 × 5 =
80
✔ LCM: 80,
GCF: 2
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## 2.
14, 6
- Prime factors:
- 14 = 2 × 7
- 6 = 2 × 3
-
GCF = common factor →
2
-
LCM = 2 × 3 × 7 =
42
✔ LCM: 42,
GCF: 2
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## 3.
3, 27
- Prime factors:
- 3 = 3
- 27 = 3³
-
GCF = smallest power of common factor →
3¹ = 3
-
LCM = highest power →
3³ = 27
✔ LCM: 27,
GCF: 3
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## 4.
6, 14
- Prime factors:
- 6 = 2 × 3
- 14 = 2 × 7
-
GCF = common factor →
2
-
LCM = 2 × 3 × 7 =
42
✔ LCM: 42,
GCF: 2
*(Same as #2 — just reversed order)*
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## 5.
16, 5
- Prime factors:
- 16 = 2⁴
- 5 = 5
-
GCF = no common prime factors →
1
-
LCM = 2⁴ × 5 = 16 × 5 =
80
✔ LCM: 80,
GCF: 1
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## 6.
8, 12
- Prime factors:
- 8 = 2³
- 12 = 2² × 3
-
GCF = min exponent of 2 →
2² = 4
-
LCM = max exponents → 2³ × 3 = 8 × 3 =
24
✔ LCM: 24,
GCF: 4
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## 7.
16, 6
- Prime factors:
- 16 = 2⁴
- 6 = 2 × 3
-
GCF = common factor →
2
-
LCM = 2⁴ × 3 = 16 × 3 =
48
✔ LCM: 48,
GCF: 2
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## 8.
8, 3
- Prime factors:
- 8 = 2³
- 3 = 3
-
GCF = no common factors →
1
-
LCM = 2³ × 3 = 8 × 3 =
24
✔ LCM: 24,
GCF: 1
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##
✔ Final Answers:
| Pair | LCM | GCF |
|----------|------|-----|
| 16, 10 | 80 | 2 |
| 14, 6 | 42 | 2 |
| 3, 27 | 27 | 3 |
| 6, 14 | 42 | 2 |
| 16, 5 | 80 | 1 |
| 8, 12 | 24 | 4 |
| 16, 6 | 48 | 2 |
| 8, 3 | 24 | 1 |
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Let me know if you’d like to see the “listing method” or a visual explanation too! 😊
Parent Tip: Review the logic above to help your child master the concept of gcf and lcm worksheet pdf.
