The number of common multiples of 6 and 15 is ______

Explanation

To find the number of common multiples of 6 and 15, we can follow these steps:

### Step 1: Identify the multiples of 6
The multiples of 6 are obtained by multiplying 6 with natural numbers:
- 1 × 6 = 6
- 2 × 6 = 12
- 3 × 6 = 18
- 4 × 6 = 24
- 5 × 6 = 30
- 6 × 6 = 36
- 7 × 6 = 42
- 8 × 6 = 48
- 9 × 6 = 54
- 10 × 6 = 60
- ... and so on.

### Step 2: Identify the multiples of 15
The multiples of 15 are obtained by multiplying 15 with natural numbers:
- 1 × 15 = 15
- 2 × 15 = 30
- 3 × 15 = 45
- 4 × 15 = 60
- 5 × 15 = 75
- 6 × 15 = 90
- 7 × 15 = 105
- 8 × 15 = 120
- 9 × 15 = 135
- 10 × 15 = 150
- ... and so on.

### Step 3: Identify the common multiples
Now, we look for the common multiples in both lists:
- From the multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
- From the multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ...

The common multiples we can see are:
- 30 (from both lists)
- 60 (from both lists)
- 90 (from both lists)
- 120 (from both lists)
- ... and so on.

### Step 4: Conclusion
Since both multiples of 6 and 15 continue indefinitely, the common multiples will also continue indefinitely. Therefore, the number of common multiples of 6 and 15 is infinite.

### Final Answer
The number of common multiples of 6 and 15 is **infinite**.

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