BMS Mathematics Academic Team Practice Test

To determine the least common multiple (LCM) of the numbers 6, 8, and 12, we first need to find their prime factorizations:

- The prime factorization of 6 is \(2^1 \times 3^1\).

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

- The prime factorization of 12 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 is \(2^3\) (from 8).

- For the prime number 3, the highest power is \(3^1\) (from both 6 and 12).

Now, we combine these:

\[

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

\]

Thus, the least common multiple of 6, 8, and 12 is 24. This answer makes sense because 24 is a multiple of each of the original numbers. It is the smallest number that can be evenly divided by 6, 8,