Let's solve each problem by finding the
Least Common Multiple (LCM) of the three given numbers. The LCM is the smallest number that is a multiple of all three numbers.
We'll use
prime factorization to find the LCM for each set.
---
1. 2, 4, 14
- Prime factors:
- 2 = 2
- 4 = 2²
- 14 = 2 × 7
Take the highest power of each prime:
- 2² × 7 = 4 × 7 =
28
✔ LCM = 28
---
2. 10, 4, 8
- Prime factors:
- 10 = 2 × 5
- 4 = 2²
- 8 = 2³
Highest powers:
- 2³ × 5 = 8 × 5 =
40
✔ LCM = 40
---
3. 24, 10, 8
- Prime factors:
- 24 = 2³ × 3
- 10 = 2 × 5
- 8 = 2³
Highest powers:
- 2³ × 3 × 5 = 8 × 3 × 5 =
120
✔ LCM = 120
---
4. 9, 6, 4
- Prime factors:
- 9 = 3²
- 6 = 2 × 3
- 4 = 2²
Highest powers:
- 2² × 3² = 4 × 9 =
36
✔ LCM = 36
---
5. 6, 3, 6
- Prime factors:
- 6 = 2 × 3
- 3 = 3
- 6 = 2 × 3
Highest powers:
- 2 × 3 =
6
✔ LCM = 6
---
6. 20, 15, 2
- Prime factors:
- 20 = 2² × 5
- 15 = 3 × 5
- 2 = 2
Highest powers:
- 2² × 3 × 5 = 4 × 3 × 5 =
60
✔ LCM = 60
---
7. 15, 16, 20
- Prime factors:
- 15 = 3 × 5
- 16 = 2⁴
- 20 = 2² × 5
Highest powers:
- 2⁴ × 3 × 5 = 16 × 3 × 5 =
240
✔ LCM = 240
---
8. 24, 9, 12
- Prime factors:
- 24 = 2³ × 3
- 9 = 3²
- 12 = 2² × 3
Highest powers:
- 2³ × 3² = 8 × 9 =
72
✔ LCM = 72
---
9. 24, 2, 4
- Prime factors:
- 24 = 2³ × 3
- 2 = 2
- 4 = 2²
Highest powers:
- 2³ × 3 = 8 × 3 =
24
✔ LCM = 24
---
10. 18, 12, 14
- Prime factors:
- 18 = 2 × 3²
- 12 = 2² × 3
- 14 = 2 × 7
Highest powers:
- 2² × 3² × 7 = 4 × 9 × 7 =
252
✔ LCM = 252
---
✔ Final Answers:
| Problem | Numbers | LCM |
|--------|--------|-----|
| 1 | 2, 4, 14 |
28 |
| 2 | 10, 4, 8 |
40 |
| 3 | 24, 10, 8 |
120 |
| 4 | 9, 6, 4 |
36 |
| 5 | 6, 3, 6 |
6 |
| 6 | 20, 15, 2 |
60 |
| 7 | 15, 16, 20 |
240 |
| 8 | 24, 9, 12 |
72 |
| 9 | 24, 2, 4 |
24 |
| 10 | 18, 12, 14 |
252 |
---
🌟 Explanation Summary:
To find the
LCM of multiple numbers:
1. Break each number into its
prime factors.
2. For each prime number, take the
highest exponent that appears in any factorization.
3. Multiply these together to get the LCM.
This method ensures you get the
smallest common multiple shared by all numbers.
Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of lcm worksheets.
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