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The problem is asking for the next time trains to Aybrin and Bleachtree will leave the station together after they initially leave at 7 am.

### Given information:
- Trains to **Aybrin** leave every 15 minutes.
- Trains to **Bleachtree** leave every 40 minutes.
- Both trains leave together initially at 7:00 am.

To find the next time they will leave together, we need to calculate the **Least Common Multiple (LCM)** of 15 and 40, which represents the interval when the trains will both be at the station at the same time.

### Step-by-step process:
1. **Prime factorization** of the intervals:
   - 15 = \( 3 \times 5 \)
   - 40 = \( 2^3 \times 5 \)
   
2. **LCM calculation**:
   - The LCM is found by taking the highest powers of all prime factors involved:
     \[
     \text{LCM}(15, 40) = 2^3 \times 3 \times 5 = 120
     \]
   
   So, the LCM of 15 and 40 is **120 minutes** (or 2 hours).

3. **Next departure time**:
   - Both trains leave together at 7:00 am. After 120 minutes (2 hours), they will leave together again at:
     \[
     7:00 \, \text{am} + 2 \, \text{hours} = 9:00 \, \text{am}
     \]

### Final Answer:
The next time both trains leave the station together will be **9:00 am**.

Would you like further explanation or have any other questions?

Here are some related questions to deepen your understanding:
1. How would the answer change if the train to Aybrin left every 20 minutes instead of 15?
2. What if both trains initially left at 8 am instead of 7 am?
3. How is the LCM used in scheduling problems like this one?
4. Can you think of a real-world scenario where such an LCM calculation is useful?
5. How can we apply the concept of greatest common divisor (GCD) to time scheduling?

**Tip:** The LCM is widely used in problems where events repeat at different intervals, like in scheduling, work shifts, or finding common periods in cyclic events.

Trains to Aybrin leave the station every 15 minutes. Trains to Bleachtree leave the station every 40 minutes. Trains to both places leave at 7am. What is the next time trains to Aybrin and Bleachtree leave the station together?

This problem involves finding the Least Common Multiple (LCM) to determine the next time two trains leave the station together. Learn how to solve LCM problems with intervals of 15 and 40 minutes, starting from 7am.

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