Let's solve each problem step-by-step to find the
Lowest Common Multiple (LCM) of the given pairs of numbers.
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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 numbers.
We can find the LCM using:
-
Prime factorization method, or
-
Listing multiples (for smaller numbers), or
-
Using the formula:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
$$
We'll use
prime factorization or
listing depending on the size of the numbers.
---
Let’s go through each pair:
---
1. 4 and 22
- Prime factors:
- 4 = 2²
- 22 = 2 × 11
- LCM = take highest powers: 2² × 11 = 4 × 11 =
44
✔ LCM = 44
---
2. 6 and 24
- 6 = 2 × 3
- 24 = 2³ × 3
- LCM = 2³ × 3 = 8 × 3 =
24
✔ LCM = 24
---
3. 8 and 6
- 8 = 2³
- 6 = 2 × 3
- LCM = 2³ × 3 = 8 × 3 =
24
✔ LCM = 24
---
4. 3 and 4
- 3 = 3
- 4 = 2²
- LCM = 2² × 3 = 4 × 3 =
12
✔ LCM = 12
---
5. 10 and 23
- 10 = 2 × 5
- 23 = prime
- No common factors → LCM = 10 × 23 =
230
✔ LCM = 230
---
6. 2 and 4
- 2 = 2
- 4 = 2²
- LCM = 2² =
4
✔ LCM = 4
---
7. 16 and 24
- 16 = 2⁴
- 24 = 2³ × 3
- LCM = 2⁴ × 3 = 16 × 3 =
48
✔ LCM = 48
---
8. 28 and 6
- 28 = 2² × 7
- 6 = 2 × 3
- LCM = 2² × 3 × 7 = 4 × 3 × 7 =
84
✔ LCM = 84
---
9. 10 and 19
- 10 = 2 × 5
- 19 = prime
- No common factors → LCM = 10 × 19 =
190
✔ LCM = 190
---
10. 14 and 28
- 14 = 2 × 7
- 28 = 2² × 7
- LCM = 2² × 7 = 4 × 7 =
28
✔ LCM = 28
---
11. 7 and 3
- Both are primes → LCM = 7 × 3 =
21
✔ LCM = 21
---
12. 4 and 29
- 4 = 2²
- 29 = prime
- No common factors → LCM = 4 × 29 =
116
✔ LCM = 116
---
13. 19 and 9
- 19 = prime
- 9 = 3²
- No common factors → LCM = 19 × 9 =
171
✔ LCM = 171
---
14. 9 and 11
- 9 = 3²
- 11 = prime
- No common factors → LCM = 9 × 11 =
99
✔ LCM = 99
---
##
✔ Final Answers:
| Problem | 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 | 28, 6 |
84 |
| 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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📝 Tips for Finding LCM:
- If one number divides the other (like 6 and 24), the larger number is the LCM.
- If the numbers are
coprime (no common factors except 1), then LCM = product of the numbers.
- Use
prime factorization for larger or trickier numbers.
Let me know if you want the worksheet filled out visually!
Parent Tip: Review the logic above to help your child master the concept of common multiples worksheet.
