To find out when the traffic lights will change simultaneously again, we need to determine the least common multiple (LCM) of the two time intervals.
The time intervals for the two traffic lights are 48 seconds and 72 seconds. To find the LCM, we can follow these steps:
Step 1: Find the prime factors of each time interval:
48 = 2^4 * 3
72 = 2^3 * 3^2
Step 2: Identify the common prime factors and their highest powers:
Common prime factors: 2^3 and 3
Highest powers: 2^4 and 3^2
Step 3: Multiply the common prime factors with their highest powers to get the LCM:
LCM = 2^4 * 3^2 = 16 * 9 = 144 seconds
So, the traffic lights will change simultaneously again after 144 seconds or 2 minutes and 24 seconds.
To find the time at which they will change simultaneously again from 7 am:
7:00 am + 2 minutes and 24 seconds = 7:02:24 am
Therefore, the traffic lights will change simultaneously again at 7:02:24 am.