Question
The least common multiple of 16 and 24 is
Answers
GPT-4o mini
To find the least common multiple (LCM) of 16 and 24, we can use the prime factorization method.
1. **Prime factorization of each number**:
- For 16: \(16 = 2^4\)
- For 24: \(24 = 2^3 \times 3^1\)
2. **Identify the highest power of each prime number in the factorizations**:
- The prime factors are 2 and 3.
- The highest power of 2 is \(2^4\) (from 16).
- The highest power of 3 is \(3^1\) (from 24).
3. **Calculate the LCM by multiplying these highest powers**:
\[
\text{LCM} = 2^4 \times 3^1 = 16 \times 3 = 48
\]
Thus, the least common multiple of 16 and 24 is **48**.
1. **Prime factorization of each number**:
- For 16: \(16 = 2^4\)
- For 24: \(24 = 2^3 \times 3^1\)
2. **Identify the highest power of each prime number in the factorizations**:
- The prime factors are 2 and 3.
- The highest power of 2 is \(2^4\) (from 16).
- The highest power of 3 is \(3^1\) (from 24).
3. **Calculate the LCM by multiplying these highest powers**:
\[
\text{LCM} = 2^4 \times 3^1 = 16 \times 3 = 48
\]
Thus, the least common multiple of 16 and 24 is **48**.