Trams

Tram no. 3,7,10,11 rode together from the depot at 5am. Tram No. 3 returns after 2 hours, tram No. 7 an hour and half, no. 10 in 45 minutes and no. 11 in 30 minutes. For how many minutes and when these trams meet again?

Result

m =  360 min
h = 11:00 hh:mm

Solution:

$$\begin{gathered} 120=2^3\cdot 3\cdot 5 \\ 90=2\cdot 3^2\cdot 5 \\ 45=3^2\cdot 5 \\ 30=2\cdot 3\cdot 5 \\ LCM(120,90,45,30)=2^3\cdot 3^2\cdot 5=360 \\ m=360\text{ min} \end{gathered}$$

$h=5+m\mathrm{/}60=11=11:00\text{ hh}:\text{mm}$

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