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:

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

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

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