Let’s solve each pair of numbers to find their
LCM (Least Common Multiple) and
GCF (Greatest Common Factor).
We’ll go one row at a time. Remember:
-
GCF is the biggest number that divides both numbers evenly.
-
LCM is the smallest number that both numbers divide into evenly.
---
1. Numbers: 16, 10
GCF:
Factors of 16: 1, 2, 4, 8, 16
Factors of 10: 1, 2, 5, 10
Common factors: 1, 2 → Greatest =
2
LCM:
Multiples of 16: 16, 32, 48, 64, 80...
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80...
First common multiple =
80
✔ LCM = 80, GCF = 2
---
2. Numbers: 14, 6
GCF:
Factors of 14: 1, 2, 7, 14
Factors of 6: 1, 2, 3, 6
Common factors: 1, 2 → Greatest =
2
LCM:
Multiples of 14: 14, 28, 42...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42...
First common multiple =
42
✔ LCM = 42, GCF = 2
---
3. Numbers: 3, 27
GCF:
3 divides 27 exactly (27 ÷ 3 = 9) → So GCF =
3
LCM:
Since 27 is a multiple of 3, LCM =
27
✔ LCM = 27, GCF = 3
---
4. Numbers: 6, 14
Same as #2 — just reversed order.
GCF: 2
LCM: 42
✔ LCM = 42, GCF = 2
---
5. Numbers: 16, 5
GCF:
16 and 5 share no common factors except 1 → GCF =
1
LCM:
Multiply them: 16 × 5 =
80 (since they have no common factors)
✔ LCM = 80, GCF = 1
---
6. Numbers: 8, 12
GCF:
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Common: 1, 2, 4 → Greatest =
4
LCM:
Multiples of 8: 8, 16, 24...
Multiples of 12: 12, 24...
First common =
24
✔ LCM = 24, GCF = 4
---
7. Numbers: 16, 6
GCF:
Factors of 16: 1, 2, 4, 8, 16
Factors of 6: 1, 2, 3, 6
Common: 1, 2 → GCF =
2
LCM:
Multiples of 16: 16, 32, 48...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
First common =
48
✔ LCM = 48, GCF = 2
---
8. Numbers: 8, 3
GCF:
No common factors except 1 → GCF =
1
LCM:
8 × 3 =
24 (no common factors)
✔ LCM = 24, GCF = 1
---
Final Answer:
16, 10 → LCM: 80, GCF: 2
14, 6 → LCM: 42, GCF: 2
3, 27 → LCM: 27, GCF: 3
6, 14 → LCM: 42, GCF: 2
16, 5 → LCM: 80, GCF: 1
8, 12 → LCM: 24, GCF: 4
16, 6 → LCM: 48, GCF: 2
8, 3 → LCM: 24, GCF: 1
Parent Tip: Review the logic above to help your child master the concept of gcf and lcm worksheet with answers.
