Let's solve each problem on the
Lowest Common Multiple (LCM) worksheet step by step. The goal is to find the
lowest common multiple of two numbers for each question.
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🔹 What is LCM?
The
Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both.
We can find the LCM using:
1.
Prime factorization method, or
2.
Listing multiples (for smaller numbers)
We’ll use
prime factorization where appropriate and
listing for simpler cases.
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✔ Let’s Solve Each Problem:
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#### 1.
4 and 22
- Prime factors:
- 4 = 2 × 2 = $2^2$
- 22 = 2 × 11
- Take highest powers: $2^2$ × 11 = 4 × 11 =
44
-
✔ LCM = 44
---
#### 2.
6 and 24
- 6 = 2 × 3
- 24 = 2³ × 3
- Highest powers: $2^3$ × 3 = 8 × 3 =
24
-
✔ LCM = 24
---
#### 3.
8 and 6
- 8 = 2³
- 6 = 2 × 3
- Highest powers: $2^3$ × 3 = 8 × 3 =
24
-
✔ LCM = 24
---
#### 4.
3 and 4
- 3 = 3
- 4 = 2²
- No common factors → multiply: 3 × 4 =
12
-
✔ LCM = 12
---
#### 5.
10 and 23
- 10 = 2 × 5
- 23 = 23 (prime)
- No common factors → multiply: 10 × 23 =
230
-
✔ LCM = 230
---
#### 6.
2 and 4
- 2 = 2
- 4 = 2²
- Highest power: $2^2$ =
4
-
✔ LCM = 4
---
#### 7.
16 and 24
- 16 = 2⁴
- 24 = 2³ × 3
- Highest powers: $2^4$ × 3 = 16 × 3 =
48
-
✔ LCM = 48
---
#### 8.
20 and 6
- 20 = 2² × 5
- 6 = 2 × 3
- Highest powers: $2^2$ × 3 × 5 = 4 × 3 × 5 =
60
-
✔ LCM = 60
---
#### 9.
10 and 19
- 10 = 2 × 5
- 19 = 19 (prime)
- No common factors → 10 × 19 =
190
-
✔ LCM = 190
---
#### 10.
14 and 28
- 14 = 2 × 7
- 28 = 2² × 7
- Highest powers: $2^2$ × 7 = 4 × 7 =
28
-
✔ LCM = 28
---
#### 11.
7 and 3
- 7 = 7
- 3 = 3
- No common factors → 7 × 3 =
21
-
✔ LCM = 21
---
#### 12.
4 and 29
- 4 = 2²
- 29 = 29 (prime)
- No common factors → 4 × 29 =
116
-
✔ LCM = 116
---
#### 13.
19 and 9
- 19 = 19 (prime)
- 9 = 3²
- No common factors → 19 × 9 =
171
-
✔ LCM = 171
---
#### 14.
9 and 11
- 9 = 3²
- 11 = 11 (prime)
- No common factors → 9 × 11 =
99
-
✔ LCM = 99
---
✔ Final Answers:
| # | Numbers | LCM |
|---|--------|-----|
| 1 | 4, 22 |
44 |
| 2 | 6, 24 |
24 |
| 3 | 8, 6 |
24 |
| 4 | 3, 4 |
12 |
| 5 | 10, 23 |
230 |
| 6 | 2, 4 |
4 |
| 7 | 16, 24 |
48 |
| 8 | 20, 6 |
60 |
| 9 | 10, 19 |
190 |
|10 | 14, 28 |
28 |
|11 | 7, 3 |
21 |
|12 | 4, 29 |
116 |
|13 | 19, 9 |
171 |
|14 | 9, 11 |
99 |
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📝 Summary Tips:
- If one number divides the other, the larger number is the LCM.
- For prime numbers, LCM = product.
- Use prime factorization to avoid listing many multiples.
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 least common multiple worksheet 4th grade.
