Let's solve each of the Least Common Multiple (LCM) problems on the worksheet step by step. The
Least Common Multiple of two numbers is the smallest number that is a multiple of both.
We'll use the
prime factorization method or the
division method to find the LCM.
---
1. LCM(25, 30)
- Prime factorization:
- 25 = 5²
- 30 = 2 × 3 × 5
- Take the highest powers of all primes: 2¹ × 3¹ × 5² = 2 × 3 × 25 =
150
✔ LCM = 150
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2. LCM(45, 25)
- 45 = 3² × 5
- 25 = 5²
- Highest powers: 3² × 5² = 9 × 25 =
225
✔ LCM = 225
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3. LCM(36, 60)
- 36 = 2² × 3²
- 60 = 2² × 3 × 5
- Highest powers: 2² × 3² × 5 = 4 × 9 × 5 =
180
✔ LCM = 180
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4. LCM(18, 27)
- 18 = 2 × 3²
- 27 = 3³
- Highest powers: 2¹ × 3³ = 2 × 27 =
54
✔ LCM = 54
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5. LCM(20, 45)
- 20 = 2² × 5
- 45 = 3² × 5
- Highest powers: 2² × 3² × 5 = 4 × 9 × 5 =
180
✔ LCM = 180
---
6. LCM(12, 36)
- 12 = 2² × 3
- 36 = 2² × 3²
- Highest powers: 2² × 3² = 4 × 9 =
36
✔ LCM = 36
---
7. LCM(24, 18)
- 24 = 2³ × 3
- 18 = 2 × 3²
- Highest powers: 2³ × 3² = 8 × 9 =
72
✔ LCM = 72
---
8. LCM(40, 20)
- 40 = 2³ × 5
- 20 = 2² × 5
- Highest powers: 2³ × 5 = 8 × 5 =
40
✔ LCM = 40
---
9. LCM(36, 18)
- 36 = 2² × 3²
- 18 = 2 × 3²
- Highest powers: 2² × 3² = 4 × 9 =
36
✔ LCM = 36
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10. LCM(25, 30)
This is the same as problem #1.
- 25 = 5²
- 30 = 2 × 3 × 5
- LCM = 2 × 3 × 5² = 2 × 3 × 25 =
150
✔ LCM = 150
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✔ Final Answers:
1. LCM(25, 30) =
150
2. LCM(45, 25) =
225
3. LCM(36, 60) =
180
4. LCM(18, 27) =
54
5. LCM(20, 45) =
180
6. LCM(12, 36) =
36
7. LCM(24, 18) =
72
8. LCM(40, 20) =
40
9. LCM(36, 18) =
36
10. LCM(25, 30) =
150
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📝 Explanation Summary:
To find the LCM:
1. Break each number into its prime factors.
2. For each prime number, take the
highest power that appears in either factorization.
3. Multiply these together.
This method ensures you get the smallest number divisible by both original numbers.
Let me know if you'd like a visual explanation or help with any specific problem!
Parent Tip: Review the logic above to help your child master the concept of common multiples worksheet.
