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The problem describes two traffic lights being installed on a street. One of them turns green every 45 seconds, and the other one turns green every 90 seconds. The question asks how long it will take for both traffic lights to turn green at the same time for the first time.

### Solution:

To find when both traffic lights will turn green simultaneously, we need to determine the Least Common Multiple (LCM) of their green intervals.

1. **Intervals of the traffic lights:**
   - First traffic light: 45 seconds
   - Second traffic light: 90 seconds

2. **Finding the LCM:**
   - Prime factorization of 45: \( 45 = 3^2 \times 5 \)
   - Prime factorization of 90: \( 90 = 2 \times 3^2 \times 5 \)

   The LCM is obtained by taking the highest power of each prime factor:
   - \( \text{LCM}(45, 90) = 2 \times 3^2 \times 5 = 90 \)

Thus, the two traffic lights will both turn green at the same time after **90 seconds**.

Would you like more details on the solution, or do you have any further questions?

Here are five related questions you might find interesting:
1. What is the general process for finding the LCM of more than two numbers?
2. How does the LCM relate to the concept of synchronization in systems?
3. Can you find the LCM of three or more time intervals?
4. How would the problem change if the intervals were not in seconds but in different units?
5. What are other practical applications of the LCM in real life?

**Tip:** When solving problems involving multiple events happening at different intervals, finding the LCM is a crucial step in determining when the events will coincide.

En una calle se están instalando dos semáforos: uno de ellos se pondrá en verde cada 45 segundos y el otro, cada minuto y medio. Una vez se conectan los semáforos, ¿cuánto tiempo tardarán en ponerse en verde al mismo tiempo por primera vez?

Learn how to calculate the time when two traffic lights will turn green at the same time, using the least common multiple (LCM). This problem involves key concepts such as prime factorization and synchronization, and is suitable for students in Grades 7-9.

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