Question
What common denominator can be used to add 1/6 and 8/15?
Answers
GPT-4o mini
To find a common denominator for the fractions \( \frac{1}{6} \) and \( \frac{8}{15} \), we need to determine the least common multiple (LCM) of the denominators (6 and 15).
First, we can find the prime factorizations of the denominators:
- \( 6 = 2 \times 3 \)
- \( 15 = 3 \times 5 \)
Now, to find the LCM, we take the highest power of each prime number from the factorizations:
- The prime factor 2 appears in \( 6 \) (to the power of 1).
- The prime factor 3 appears in both \( 6 \) and \( 15 \) (the maximum power is 1).
- The prime factor 5 appears in \( 15 \) (to the power of 1).
Now we multiply these together:
\[
\text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30
\]
Thus, the least common denominator (LCD) for the fractions \( \frac{1}{6} \) and \( \frac{8}{15} \) is \( 30 \).
Therefore, the common denominator is \( \boxed{30} \).
First, we can find the prime factorizations of the denominators:
- \( 6 = 2 \times 3 \)
- \( 15 = 3 \times 5 \)
Now, to find the LCM, we take the highest power of each prime number from the factorizations:
- The prime factor 2 appears in \( 6 \) (to the power of 1).
- The prime factor 3 appears in both \( 6 \) and \( 15 \) (the maximum power is 1).
- The prime factor 5 appears in \( 15 \) (to the power of 1).
Now we multiply these together:
\[
\text{LCM} = 2^1 \times 3^1 \times 5^1 = 2 \times 3 \times 5 = 30
\]
Thus, the least common denominator (LCD) for the fractions \( \frac{1}{6} \) and \( \frac{8}{15} \) is \( 30 \).
Therefore, the common denominator is \( \boxed{30} \).