Let's solve each of these 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(8, 12)
- Prime factors:
- 8 = 2³
- 12 = 2² × 3
- Take the highest power of each prime:
- 2³ × 3 = 8 × 3 =
24
✔ LCM(8, 12) = 24
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2) LCM(20, 40)
- Prime factors:
- 20 = 2² × 5
- 40 = 2³ × 5
- Highest powers: 2³ × 5 = 8 × 5 =
40
✔ LCM(20, 40) = 40
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3) 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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4) 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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5) LCM(42, 30)
- Prime factors:
- 42 = 2 × 3 × 7
- 30 = 2 × 3 × 5
- Highest powers: 2 × 3 × 5 × 7 =
210
✔ LCM(42, 30) = 210
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6) LCM(24, 32)
- Prime factors:
- 24 = 2³ × 3
- 32 = 2⁵
- Highest powers: 2⁵ × 3 = 32 × 3 =
96
✔ LCM(24, 32) = 96
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7) LCM(15, 9)
- Prime factors:
- 15 = 3 × 5
- 9 = 3²
- Highest powers: 3² × 5 = 9 × 5 =
45
✔ LCM(15, 9) = 45
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8) LCM(45, 27)
- Prime factors:
- 45 = 3² × 5
- 27 = 3³
- Highest powers: 3³ × 5 = 27 × 5 =
135
✔ LCM(45, 27) = 135
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9) LCM(34, 26)
- Prime factors:
- 34 = 2 × 17
- 26 = 2 × 13
- Highest powers: 2 × 13 × 17 = 2 × 221 =
442
✔ LCM(34, 26) = 442
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10) LCM(10, 48)
- Prime factors:
- 10 = 2 × 5
- 48 = 2⁴ × 3
- Highest powers: 2⁴ × 3 × 5 = 16 × 3 × 5 = 48 × 5 =
240
✔ LCM(10, 48) = 240
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✔ Final Answers:
1) LCM(8, 12) =
24
2) LCM(20, 40) =
40
3) LCM(22, 6) =
66
4) LCM(14, 4) =
28
5) LCM(42, 30) =
210
6) LCM(24, 32) =
96
7) LCM(15, 9) =
45
8) LCM(45, 27) =
135
9) LCM(34, 26) =
442
10) LCM(10, 48) =
240
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Let me know if you'd like a visual explanation or practice tips!
Parent Tip: Review the logic above to help your child master the concept of lcm worksheets.
