To solve the problem of determining when the traffic lights will next change simultaneously after 12 noon, we need to find the least common multiple (LCM) of the given time intervals.
### Step-by-Step Solution
1. Convert Time Intervals to Seconds:
- First interval: 1 minute = 60 seconds.
- Second interval: 1 minute 20 seconds = (1 60) + 20 = 80 seconds.
- Third interval: 2 minutes = 2 60 = 120 seconds.
2. Find the LCM of the Three Intervals in Seconds:
To find when the traffic lights will next change together, we need to calculate the least common multiple (LCM) of 60 seconds, 80 seconds, and 120 seconds. The LCM of these values is 240 seconds.
3. Convert the LCM Back to Minutes and Seconds:
- 240 seconds is equivalent to 4 minutes (since 240 ÷ 60 = 4).
4. Determine the Time After the LCM Interval:
- We start at 12 noon.
- Adding 4 minutes to 12:00 noon gives us 12:04 PM.
So, the next time the traffic lights will change simultaneously after starting at 12 noon is at 12:04 PM.
