Find the first four common multiples of 6, 8, and 12

To find the first four common multiples of 6, 8, and 12, we need to identify the least common multiple (LCM) of these numbers, and then multiply it by 1, 2, 3, and 4 to get the first four common multiples.

### Step 1: Find the prime factorization of each number.
- 6 = 2 × 3
- 8 = 2³
- 12 = 2² × 3

### Step 2: Take the highest powers of all prime factors.
- The highest power of 2 is 2³ (from 8).
- The highest power of 3 is 3¹ (from 6 or 12).

So, the least common multiple (LCM) is:
\[
\text{LCM}(6, 8, 12) = 2^3 \times 3 = 24
\]

### Step 3: Multiply the LCM by 1, 2, 3, and 4 to get the first four common multiples.
- 24 × 1 = 24
- 24 × 2 = 48
- 24 × 3 = 72
- 24 × 4 = 96

Thus, the first four common multiples of 6, 8, and 12 are:
\[
24, 48, 72, 96
\]

Do you want further details or have any questions? Here are some related problems:

1. What is the least common multiple (LCM) of 15, 20, and 30?
2. Find the first five common multiples of 9 and 12.
3. Determine the LCM of 7, 14, and 21.
4. What are the first four common multiples of 5 and 10?
5. How can you quickly find the LCM of large numbers?

**Tip:** To find the least common multiple (LCM), always take the highest powers of all prime factors involved.

Learn how to find the first four common multiples of 6, 8, and 12 using the least common multiple (LCM). This solution walks through prime factorization, finding LCM, and multiplying to get the multiples. Suitable for students in Grades 5-7.

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