Question

The first five multiples for the numbers 4 and 6 are shown below.

Multiples of 4: 4, 8, 12, 16, 20, . . .
Multiples of 6: 6, 12, 18, 24, 30, . . .

What is the least common multiple of 4 and 6?
2
4
12
24

Answer 1

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**.