Let’s solve each problem step by step. We’re finding either the
GCF (Greatest Common Factor) or
LCM (Least Common Multiple) of two numbers.
---
1) GCF [30, 30]
The greatest common factor is the largest number that divides both numbers evenly.
Since both numbers are the same (30 and 30), the biggest number that divides them is 30 itself.
✔ GCF = 30
---
2) LCM [5, 12]
LCM is the smallest number that both 5 and 12 divide into evenly.
Multiples of 5: 5, 10, 15, 20, 25,
30, 35, 40, 45,
60...
Multiples of 12: 12, 24, 36, 48,
60...
First common multiple is 60.
✔ LCM = 60
---
3) GCF [24, 24]
Same number → GCF is the number itself.
✔ GCF = 24
---
4) LCM [14, 21]
List multiples:
14: 14, 28,
42, 56...
21: 21,
42, 63...
Smallest common multiple is 42.
Alternatively:
Prime factors:
14 = 2 × 7
21 = 3 × 7
LCM = 2 × 3 × 7 = 42
✔ LCM = 42
---
5) GCF [22, 77]
Factors of 22: 1, 2, 11, 22
Factors of 77: 1, 7, 11, 77
Common factors: 1, 11 → Greatest is 11.
Or prime factors:
22 = 2 × 11
77 = 7 × 11
Common factor: 11
✔ GCF = 11
---
6) LCM [16, 4]
Since 16 is a multiple of 4 (4 × 4 = 16), the LCM is 16.
Check: Multiples of 4: 4, 8, 12, 16... → yes, 16 works.
✔ LCM = 16
---
7) GCF [52, 59]
52 factors: 1, 2, 4, 13, 26, 52
59 is a prime number → factors: 1, 59
Only common factor is 1.
✔ GCF = 1
---
8) LCM [32, 24]
Prime factors:
32 = 2⁵
24 = 2³ × 3
LCM = take highest powers: 2⁵ × 3 = 32 × 3 = 96
Check:
Multiples of 32: 32, 64, 96...
Multiples of 24: 24, 48, 72, 96... → matches!
✔ LCM = 96
---
9) GCF [48, 68]
Prime factors:
48 = 2⁴ × 3
68 = 2² × 17
Common: 2² = 4
Check factors:
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
68: 1, 2, 4, 17, 34, 68
Common: 1, 2, 4 → GCF = 4
✔ GCF = 4
---
10) LCM [5, 15]
15 is a multiple of 5 (5 × 3 = 15), so LCM is 15.
✔ LCM = 15
---
Final Answer:
1) 30
2) 60
3) 24
4) 42
5) 11
6) 16
7) 1
8) 96
9) 4
10) 15
Parent Tip: Review the logic above to help your child master the concept of gcd lcm worksheets.
