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What is the least common multiple of 6 and 8?

24

To determine the least common multiple (LCM) of the numbers 6 and 8, we start by finding their prime factorizations:

- The prime factorization of 6 is \(2 \times 3\).

- The prime factorization of 8 is \(2^3\).

Next, we identify the highest power of each prime number that appears in these factorizations:

- For the prime number 2, the highest power between the factorizations is \(2^3\) (from 8).

- For the prime number 3, the highest power is \(3^1\) (from 6).

The LCM is found by multiplying these highest powers together:

\[

LCM = 2^3 \times 3^1 = 8 \times 3 = 24.

\]

Therefore, the least common multiple of 6 and 8 is 24. This result shows that 24 is the smallest number that both 6 and 8 can divide without leaving a remainder, confirming that this is indeed the correct answer.

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