Question
The least common multiple of 12 and 24 is
Answers
GPT-4o mini
To find the least common multiple (LCM) of 12 and 24, we can start by identifying the prime factorizations of both numbers:
- 12 can be factored into primes as \( 12 = 2^2 \times 3^1 \).
- 24 can be factored into primes as \( 24 = 2^3 \times 3^1 \).
Next, to find the LCM, we take the highest power of each prime factor that appears in any of the factorizations:
- The highest power of 2 is \( 2^3 \) (from 24).
- The highest power of 3 is \( 3^1 \) (which appears in both).
Now, we multiply these together to find the LCM:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]
Thus, the least common multiple of 12 and 24 is \( \boxed{24} \).
- 12 can be factored into primes as \( 12 = 2^2 \times 3^1 \).
- 24 can be factored into primes as \( 24 = 2^3 \times 3^1 \).
Next, to find the LCM, we take the highest power of each prime factor that appears in any of the factorizations:
- The highest power of 2 is \( 2^3 \) (from 24).
- The highest power of 3 is \( 3^1 \) (which appears in both).
Now, we multiply these together to find the LCM:
\[
\text{LCM} = 2^3 \times 3^1 = 8 \times 3 = 24
\]
Thus, the least common multiple of 12 and 24 is \( \boxed{24} \).