Let's solve the
Lowest Common Multiple (LCM) worksheet step by step.
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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:
-
Listing multiples (for small numbers)
-
Prime factorization
- Or
using the formula:
$$
\text{LCM}(a, b) = \frac{a \times b}{\text{GCF}(a, b)}
$$
We’ll use the
prime factorization method or
listing multiples, depending on the numbers.
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Now let’s go through each problem:
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1. 4 and 22
- Prime factors:
- 4 = 2 × 2 = $2^2$
- 22 = 2 × 11
- LCM = $2^2 × 11 = 4 × 11 = \boxed{44}$
✔ Answer: 44
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2. 6 and 24
- 6 = 2 × 3
- 24 = 2³ × 3
- LCM = $2^3 × 3 = 8 × 3 = \boxed{24}$
✔ Answer: 24
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3. 8 and 6
- 8 = 2³
- 6 = 2 × 3
- LCM = $2^3 × 3 = 8 × 3 = \boxed{24}$
✔ Answer: 24
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4. 3 and 4
- 3 = 3
- 4 = 2²
- LCM = $2^2 × 3 = 4 × 3 = \boxed{12}$
✔ Answer: 12
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5. 10 and 23
- 10 = 2 × 5
- 23 = prime
- Since they have no common factors, LCM = $10 × 23 = \boxed{230}$
✔ Answer: 230
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6. 2 and 4
- 2 = 2
- 4 = 2²
- LCM = $2^2 = \boxed{4}$
✔ Answer: 4
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7. 16 and 24
- 16 = 2⁴
- 24 = 2³ × 3
- LCM = $2^4 × 3 = 16 × 3 = \boxed{48}$
✔ Answer: 48
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8. 20 and 6
- 20 = 2² × 5
- 6 = 2 × 3
- LCM = $2^2 × 3 × 5 = 4 × 3 × 5 = \boxed{60}$
✔ Answer: 60
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9. 10 and 19
- 10 = 2 × 5
- 19 = prime
- No common factors → LCM = $10 × 19 = \boxed{190}$
✔ Answer: 190
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10. 14 and 28
- 14 = 2 × 7
- 28 = 2² × 7
- LCM = $2^2 × 7 = 4 × 7 = \boxed{28}$
✔ Answer: 28
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11. 7 and 3
- Both are prime
- LCM = $7 × 3 = \boxed{21}$
✔ Answer: 21
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12. 4 and 29
- 4 = 2²
- 29 = prime
- LCM = $4 × 29 = \boxed{116}$
✔ Answer: 116
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13. 19 and 9
- 19 = prime
- 9 = 3²
- No common factors → LCM = $19 × 9 = \boxed{171}$
✔ Answer: 171
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14. 9 and 11
- 9 = 3²
- 11 = prime
- LCM = $9 × 11 = \boxed{99}$
✔ Answer: 99
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✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 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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📝 Tips for Students:
- If one number divides the other (e.g., 6 and 24), the LCM is the larger number.
- For
prime numbers, just multiply them together.
- Use
prime factorization to avoid listing too 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 practice worksheet.
