What is the least common multiple of 6 and 8?

To find the least common multiple (LCM) of 6 and 8, we begin by listing the multiples of each number.

The multiples of 6 are:

6, 12, 18, 24, 30, ...

The multiples of 8 are:

8, 16, 24, 32, ...

Next, we look for the smallest multiple that appears in both lists. The first common multiple we encounter is 24, making it the least common multiple.

We can also confirm this using prime factorization. The number 6 can be expressed as 2 x 3, and the number 8 can be expressed as 2^3. To find the LCM, we take the highest power of each prime factor present in both factorizations.

For the prime factor 2, the highest power is 2^3 (from 8), and for the prime factor 3, the highest power is 3^1 (from 6). Thus, the LCM is calculated as:

2^3 x 3^1 = 8 x 3 = 24.

Both methods confirm that the least common multiple of 6 and 8 is indeed 24. This reasoning