Let's solve each of the Least Common Multiple (LCM) problems step by step.
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What is LCM?
The
Least Common Multiple (LCM) of two numbers is the smallest positive number that is divisible by both numbers.
We can find the LCM using:
-
Prime factorization method, or
-
Listing multiples (for smaller numbers)
We’ll use prime factorization for accuracy and efficiency.
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1) LCM(9, 15)
- Prime factors:
- 9 = 3²
- 15 = 3 × 5
- Take highest powers: 3² × 5 = 9 × 5 =
45
✔ LCM(9, 15) = 45
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2) LCM(4, 8)
- Prime factors:
- 4 = 2²
- 8 = 2³
- Highest power: 2³ =
8
✔ LCM(4, 8) = 8
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3) LCM(18, 3)
- Prime factors:
- 18 = 2 × 3²
- 3 = 3¹
- Highest powers: 2 × 3² = 2 × 9 =
18
✔ LCM(18, 3) = 18
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4) LCM(22, 6)
- Prime factors:
- 22 = 2 × 11
- 6 = 2 × 3
- Highest powers: 2 × 3 × 11 =
66
✔ LCM(22, 6) = 66
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5) LCM(9, 21)
- Prime factors:
- 9 = 3²
- 21 = 3 × 7
- Highest powers: 3² × 7 = 9 × 7 =
63
✔ LCM(9, 21) = 63
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6) LCM(2, 3)
- Prime factors:
- 2 = 2
- 3 = 3
- No common factors → LCM = 2 × 3 =
6
✔ LCM(2, 3) = 6
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7) LCM(14, 4)
- Prime factors:
- 14 = 2 × 7
- 4 = 2²
- Highest powers: 2² × 7 = 4 × 7 =
28
✔ LCM(14, 4) = 28
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8) LCM(5, 25)
- Prime factors:
- 5 = 5
- 25 = 5²
- Highest power: 5² =
25
✔ LCM(5, 25) = 25
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9) LCM(7, 6)
- Prime factors:
- 7 = 7
- 6 = 2 × 3
- All primes: 2 × 3 × 7 =
42
✔ LCM(7, 6) = 42
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10) LCM(12, 20)
- Prime factors:
- 12 = 2² × 3
- 20 = 2² × 5
- Highest powers: 2² × 3 × 5 = 4 × 3 × 5 =
60
✔ LCM(12, 20) = 60
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✔ Final Answers:
| Problem | LCM |
|--------|-----|
| 1) LCM(9, 15) |
45 |
| 2) LCM(4, 8) |
8 |
| 3) LCM(18, 3) |
18 |
| 4) LCM(22, 6) |
66 |
| 5) LCM(9, 21) |
63 |
| 6) LCM(2, 3) |
6 |
| 7) LCM(14, 4) |
28 |
| 8) LCM(5, 25) |
25 |
| 9) LCM(7, 6) |
42 |
| 10) LCM(12, 20) |
60 |
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You can now fill in the blanks on the worksheet with these answers. Let me know if you'd like a printable version or explanation in another format!
Parent Tip: Review the logic above to help your child master the concept of least common multiple and greatest common factor worksheets.
