## Task B-1.4.

From the starting tram station, three trams depart at 5:00 AM. The first tram takes 1 hour and 30 minutes to return to the starting station, the second tram takes 1 hour, and the third tram takes 40 minutes. At what time will all three trams be at the starting station at the same time again? How many times will this happen on the same day if the trams operate from 5:00 AM to 24:00 (midnight), not counting the first departure at 5:00 AM?
## First solution.

The time required for all three trams to return to the starting station at the same time after a joint departure is the least common multiple of the times each tram individually needs to return to the starting station.

Thus, we are looking for the least common multiple of

1 hour and 30 minutes $=90$ minutes, 1 hour $=60$ minutes, and 40 minutes, which is the number:

$LCM(90,60,40)=10 \cdot 3 \cdot 3 \cdot 2 \cdot 2=360$.

The trams will meet at the starting station every 360 minutes, or every 6 hours.

They will first meet again at the starting station at 11:00.

They will meet at the starting station 3 times in the same day.

1 point