# What is the least common multiple of #{8, 12, 16, 3}?

48

Let's first do prime factorizations:

Now we look for the largest grouping of each prime in the factorizations.

For the number 2, the largest grouping is in 16:

The other prime factor is 3. We need one of those (since both 12 and 3 only have one):

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To find the least common multiple (LCM) of a set of numbers, first, find the prime factorization of each number. Then, identify the highest power of each prime factor that appears in any of the factorizations, and multiply these powers together.

Prime factorization of each number: 8 = 2^3 12 = 2^2 * 3 16 = 2^4 3 = 3^1

Now, identify the highest power of each prime factor:

- The highest power of 2 is 4 (from 16).
- The highest power of 3 is 1 (from 3).

Multiply these powers together: LCM = 2^4 * 3^1 LCM = 16 * 3 LCM = 48

Therefore, the least common multiple of {8, 12, 16, 3} is 48.

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