Question
The least common multiple of 18 and 12 is
Answers
GPT-4o mini
To find the least common multiple (LCM) of 18 and 12, we can use the prime factorization method.
First, let's find the prime factorization of each number:
- The prime factorization of 18 is \( 2^1 \times 3^2 \).
- The prime factorization of 12 is \( 2^2 \times 3^1 \).
To find the LCM, we take the highest power of each prime factor that appears in the factorizations:
- For the prime number 2: The highest power is \( 2^2 \) (from 12).
- For the prime number 3: The highest power is \( 3^2 \) (from 18).
Now, we multiply these together to find the LCM:
\[
\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36.
\]
Thus, the least common multiple of 18 and 12 is \( \boxed{36} \).
First, let's find the prime factorization of each number:
- The prime factorization of 18 is \( 2^1 \times 3^2 \).
- The prime factorization of 12 is \( 2^2 \times 3^1 \).
To find the LCM, we take the highest power of each prime factor that appears in the factorizations:
- For the prime number 2: The highest power is \( 2^2 \) (from 12).
- For the prime number 3: The highest power is \( 3^2 \) (from 18).
Now, we multiply these together to find the LCM:
\[
\text{LCM} = 2^2 \times 3^2 = 4 \times 9 = 36.
\]
Thus, the least common multiple of 18 and 12 is \( \boxed{36} \).