What is the least common multiple of 8 and 12?

To determine the least common multiple (LCM) of 8 and 12, we start by identifying the multiples of each number.

For 8, the multiples are:

8, 16, 24, 32, 40, ...

For 12, the multiples are:

12, 24, 36, 48, ...

Next, we look for the smallest multiple that appears in both lists. The first common multiple between the two lists is 24.

To further validate this result, we can use prime factorization. The prime factorization of 8 is (2^3) and for 12, it is (2^2 \times 3^1). The LCM is found by taking the highest power of each prime that appears in the factorizations.

• For the prime number 2, the highest power between 8 and 12 is (2^3) (from 8).

• For the prime number 3, the highest power is (3^1) (from 12).

Now, we combine these to find the LCM:

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