Tram lines

Trams of five lines are driven at intervals of 5,8,10,12, and 15 minutes. At 12 o'clock, come out of the station at the same time. How many hours will we all meet again? How many times has each tram passed for this stop?

Final Answer:

t =  2 h
a =  24
b =  15
c =  12
d =  10
e =  8

Step-by-step explanation:

$$\begin{gathered} 5...\text{ prime number} \\ 8=2^3 \\ 10=2\cdot 5 \\ 12=2^2\cdot 3 \\ 15=3\cdot 5 \\ LCM(5,8,10,12,15)=2^3\cdot 3\cdot 5=120 \\ m=LCM(5,8,10,12,15)=120 \\ t=m/60=120/60=2\text{h} \end{gathered}$$

$a=m/5=120/5=24$

$b=m/8=120/8=15$

$c=m/10=120/10=12$

$d=m/12=120/12=10$

$e=m/15=120/15=8$

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