Algebra Practice Test 2025 – The Complete Guide to Mastering Your Exam Success!

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Question: 1 / 400

How do you find the least common multiple (LCM) of 12 and 18?

LCM = 18

LCM = 24

LCM = 36

To find the least common multiple (LCM) of 12 and 18, the most straightforward approach is to use the prime factorization method.

First, we can factor both numbers into their prime components:

- The prime factorization of 12 is \(2^2 \times 3^1\).

- The prime factorization of 18 is \(2^1 \times 3^2\).

To determine the LCM, we take the highest power of each prime number present in the factorizations:

- For the prime number 2, the highest power in the factorizations is \(2^2\) (from 12).

- For the prime number 3, the highest power is \(3^2\) (from 18).

Now, we multiply these together to find the LCM:

\[

LCM = 2^2 \times 3^2 = 4 \times 9 = 36.

\]

Thus, the least common multiple of 12 and 18 is 36. This is why the correct answer is identified as 36. Understanding the prime factorization method not only clarifies how to find LCM but also provides a consistent technique for tackling similar

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LCM = 54

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