Let’s solve each problem step by step. We’re finding the
Least Common Multiple (LCM) — that means the smallest number that all the given numbers can divide into evenly.
We’ll go one by one:
---
1. LCM of 20, 10, 30
Multiples of 20: 20, 40, 60, 80...
Multiples of 10: 10, 20, 30, 40, 50, 60...
Multiples of 30: 30, 60, 90...
First common multiple? →
60
✔ LCM(20, 10, 30) =
60
---
2. LCM of 15, 25, 30
Break them down to prime factors:
- 15 = 3 × 5
- 25 = 5 × 5
- 30 = 2 × 3 × 5
Take highest power of each prime:
→ 2¹, 3¹, 5² → 2 × 3 × 25 =
150
✔ LCM(15, 25, 30) =
150
---
3. LCM of 12, 36, 20
Prime factors:
- 12 = 2² × 3
- 36 = 2² × 3²
- 20 = 2² × 5
Highest powers: 2², 3², 5 → 4 × 9 × 5 =
180
✔ LCM(12, 36, 20) =
180
---
4. LCM of 25, 40, 30
Prime factors:
- 25 = 5²
- 40 = 2³ × 5
- 30 = 2 × 3 × 5
Highest powers: 2³, 3¹, 5² → 8 × 3 × 25 =
600
✔ LCM(25, 40, 30) =
600
---
5. LCM of 25, 20, 15
Prime factors:
- 25 = 5²
- 20 = 2² × 5
- 15 = 3 × 5
Highest powers: 2², 3¹, 5² → 4 × 3 × 25 =
300
✔ LCM(25, 20, 15) =
300
---
6. LCM of 36, 12, 45
Prime factors:
- 36 = 2² × 3²
- 12 = 2² × 3
- 45 = 3² × 5
Highest powers: 2², 3², 5 → 4 × 9 × 5 =
180
✔ LCM(36, 12, 45) =
180
---
7. LCM of 24, 9, 15
Prime factors:
- 24 = 2³ × 3
- 9 = 3²
- 15 = 3 × 5
Highest powers: 2³, 3², 5 → 8 × 9 × 5 =
360
✔ LCM(24, 9, 15) =
360
---
8. LCM of 20, 10, 15
Prime factors:
- 20 = 2² × 5
- 10 = 2 × 5
- 15 = 3 × 5
Highest powers: 2², 3¹, 5 → 4 × 3 × 5 =
60
✔ LCM(20, 10, 15) =
60
---
9. LCM of 24, 36, 12
Prime factors:
- 24 = 2³ × 3
- 36 = 2² × 3²
- 12 = 2² × 3
Highest powers: 2³, 3² → 8 × 9 =
72
✔ LCM(24, 36, 12) =
72
---
10. LCM of 45, 25, 50
Prime factors:
- 45 = 3² × 5
- 25 = 5²
- 50 = 2 × 5²
Highest powers: 2¹, 3², 5² → 2 × 9 × 25 =
450
✔ LCM(45, 25, 50) =
450
---
Final Answer:
1. 60
2. 150
3. 180
4. 600
5. 300
6. 180
7. 360
8. 60
9. 72
10. 450
Parent Tip: Review the logic above to help your child master the concept of lcm worksheet 5th grade.
