What is the least common multiple (LCM) of 8 and 12?

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To find the least common multiple (LCM) of 8 and 12, we start by determining the prime factorization of both numbers.

For 8, the prime factorization is (2^3) since (8 = 2 \times 2 \times 2).

For 12, the prime factorization is (2^2 \times 3) because (12 = 2 \times 2 \times 3).

The LCM is found by taking the highest powers of all prime factors present in the factorizations.

For the prime factor 2, the highest power in our factorizations is (2^3) (from 8).
For the prime factor 3, the highest power is (3^1) (from 12).

Now we multiply these highest powers together to find the LCM:

[

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

]

Thus, the least common multiple of 8 and 12 is 24. This makes the correct answer 24, which aligns with the choice provided.