2) Clay takes private soccer lessons every 9 days and piano lessons every * 3 points 6 days. In how many days will she have both piano and soccer on the same day? 2 6 18 54

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UpStudy AI · Accepted Answer

To find out when Clay will have both soccer and piano lessons on the same day, we need to determine the least common multiple (LCM) of the two lesson intervals: 9 days for soccer and 6 days for piano.

### Step 1: Identify the lesson intervals
- Soccer lessons: $$ S = 9 $$ days
- Piano lessons: $$ P = 6 $$ days

### Step 2: Find the LCM of 9 and 6
The LCM of two numbers is the smallest number that is a multiple of both.

1. **List the multiples of each number:**
   - Multiples of 9: $$ 9, 18, 27, 36, 45, 54, \ldots $$
   - Multiples of 6: $$ 6, 12, 18, 24, 30, 36, 42, 48, 54, \ldots $$

2. **Identify the smallest common multiple:**
   - The common multiples from the lists are $$ 18, 36, 54, \ldots $$
   - The smallest common multiple is $$ 18 $$.

### Conclusion
Clay will have both soccer and piano lessons on the same day in **18 days**.

Thus, the answer is $$ 18 $$.
Clay will have both soccer and piano lessons on the same day in 18 days.

Clay takes private soccer lessons every 9 days and piano lessons every * 3 points
6 days. In how many days will she have both piano and soccer on the
same day?
2
6
18
54

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