Question
The lowest common denominator of 1/2, 1/3, and 1/4 is:
24
12
6
24
12
6
Answers
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Answered by
GPT-4o mini
To find the lowest common denominator (LCD) of the fractions \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \), we need to determine the least common multiple (LCM) of the denominators 2, 3, and 4.
1. **Prime Factorization**:
- \( 2 = 2^1 \)
- \( 3 = 3^1 \)
- \( 4 = 2^2 \)
2. **Identify the highest power of each prime factor**:
- For \( 2 \): the highest power is \( 2^2 \) (from 4).
- For \( 3 \): the highest power is \( 3^1 \) (from 3).
3. **Multiply the highest powers together**:
\[
\text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12
\]
Therefore, the lowest common denominator of \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \) is **12**.
1. **Prime Factorization**:
- \( 2 = 2^1 \)
- \( 3 = 3^1 \)
- \( 4 = 2^2 \)
2. **Identify the highest power of each prime factor**:
- For \( 2 \): the highest power is \( 2^2 \) (from 4).
- For \( 3 \): the highest power is \( 3^1 \) (from 3).
3. **Multiply the highest powers together**:
\[
\text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12
\]
Therefore, the lowest common denominator of \( \frac{1}{2}, \frac{1}{3}, \) and \( \frac{1}{4} \) is **12**.
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