To find the least common multiple (LCM) of 4 and 6, we can list the first few multiples of each number, or use the prime factorization method.
Method 1: Listing Multiples
- Multiples of 4: 4, 8, 12, 16, 20, ...
- Multiples of 6: 6, 12, 18, 24, 30, ...
From the lists, the smallest common multiple is 12.
Method 2: Prime Factorization
- The prime factorization of 4 is \(2^2\).
- The prime factorization of 6 is \(2^1 \times 3^1\).
To find the LCM, take the highest power of each prime factor:
- For the prime number 2, the highest power from both factorizations is \(2^2\).
- For the prime number 3, the highest power is \(3^1\).
Now multiply the highest powers together: \[ LCM = 2^2 \times 3^1 = 4 \times 3 = 12 \]
Conclusion
The least common multiple of 4 and 6 is 12.