It looks like you've uploaded a worksheet titled
"Least Common Multiple" with a series of problems asking to find the
LCM (Least Common Multiple) of pairs of numbers. Since I can't view images directly, I’ll help you solve this step-by-step based on the text you provided.
Let’s go through each problem and find the LCM of the given pairs of numbers. The LCM is the smallest number that is a multiple of both numbers.
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How to Find LCM:
There are several methods:
1.
List multiples until you find the smallest common one.
2.
Prime factorization: Break down each number into prime factors, then take the highest power of each prime.
3.
Use the formula:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
$$
We'll use
prime factorization for efficiency.
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Problem Set:
#### 1. 6, 10
- Prime factors:
- 6 = 2 × 3
- 10 = 2 × 5
- Take highest powers: 2, 3, 5 → 2 × 3 × 5 =
30
✔ LCM = 30
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#### 2. 4, 8
- 4 = 2²
- 8 = 2³
- Highest power: 2³ =
8
✔ LCM = 8
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#### 3. 15, 9
- 15 = 3 × 5
- 9 = 3²
- Highest powers: 3² × 5 = 9 × 5 =
45
✔ LCM = 45
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#### 4. 16, 4
- 16 = 2⁴
- 4 = 2²
- Highest power: 2⁴ =
16
✔ LCM = 16
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#### 5. 18, 3
- 18 = 2 × 3²
- 3 = 3¹
- Highest powers: 2 × 3² = 2 × 9 =
18
✔ LCM = 18
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#### 6. 2, 7
- 2 and 7 are both prime
- LCM = 2 × 7 =
14
✔ LCM = 14
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#### 7. 25, 5
- 25 = 5²
- 5 = 5¹
- Highest power: 5² =
25
✔ LCM = 25
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#### 8. 12, 18
- 12 = 2² × 3
- 18 = 2 × 3²
- Highest powers: 2² × 3² = 4 × 9 =
36
✔ LCM = 36
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#### 9. 14, 4
- 14 = 2 × 7
- 4 = 2²
- Highest powers: 2² × 7 = 4 × 7 =
28
✔ LCM = 28
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#### 10. 6, 25
- 6 = 2 × 3
- 25 = 5²
- All primes: 2, 3, 5² → 2 × 3 × 25 =
150
✔ LCM = 150
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#### 11. 7, 8
- 7 = 7
- 8 = 2³
- No common factors → 7 × 8 =
56
✔ LCM = 56
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#### 12. 12, 20
- 12 = 2² × 3
- 20 = 2² × 5
- Highest powers: 2² × 3 × 5 = 4 × 3 × 5 =
60
✔ LCM = 60
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✔ Final Answers:
| Problem | Numbers | LCM |
|--------|---------|-----|
| 1 | 6, 10 | 30 |
| 2 | 4, 8 | 8 |
| 3 | 15, 9 | 45 |
| 4 | 16, 4 | 16 |
| 5 | 18, 3 | 18 |
| 6 | 2, 7 | 14 |
| 7 | 25, 5 | 25 |
| 8 | 12, 18 | 36 |
| 9 | 14, 4 | 28 |
| 10 | 6, 25 | 150 |
| 11 | 7, 8 | 56 |
| 12 | 12, 20 | 60 |
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📝 Summary:
The
Least Common Multiple (LCM) is found by identifying the highest powers of all prime factors present in the numbers. This method works efficiently for any pair of numbers.
Let me know if you'd like a printable version or explanation using another method (like listing multiples)!
Parent Tip: Review the logic above to help your child master the concept of find the lcm worksheet.
