To find the least common multiple (LCM) of 2, 3, and 4, we can start by determining the prime factorization of each number:
- The prime factorization of 2 is \(2\).
- The prime factorization of 3 is \(3\).
- The prime factorization of 4 is \(2^2\).
Next, we take the highest power of each prime number that appears in these factorizations:
- The highest power of \(2\) is \(2^2\) (from 4).
- The highest power of \(3\) is \(3^1\) (from 3).
Now we can calculate the LCM by multiplying these together:
\[ LCM = 2^2 \times 3^1 = 4 \times 3 = 12 \]
Thus, the LCM of 2, 3, and 4 is 12.