At Eglinton subway station the 54 Lawrence bus leaves the station every 18 minutes. The 34 Eglinton Bus leaves every 30 minutes. The 28 Mt Pleasant Bus leaves the station every 11 minutes. Assuming the buses run 24 hours a day at what time interval do all three buses leave the station together?(Show all steps, write the answer in hours)

To find the time interval when all three buses leave the station together, we need to find the LCM (Least Common Multiple) of the time intervals for each bus.

Step 1: Convert the time intervals to the same unit (minutes in this case).
- The time interval for the 54 Lawrence bus is 18 minutes.
- The time interval for the 34 Eglinton bus is 30 minutes.
- The time interval for the 28 Mt Pleasant bus is 11 minutes.

Step 2: Find the LCM of these time intervals.
To find the LCM, we can list the multiples of each time interval until we find a common multiple.

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, ...
Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, ...

From the lists above, we can see that the least common multiple is 90 minutes.

Step 3: Convert the answer to hours.
Since the time intervals were given in minutes, we need to convert the LCM to hours by dividing it by 60 (since there are 60 minutes in an hour).
90 minutes divided by 60 = 1.5 hours.

Therefore, all three buses leave the station together every 1.5 hours.