# Bus lines

Buses connections are started from bus stop on its regular circuit as follows: No. 27 bus every 27 minutes and No.18 every half hour. What time started this two bus lines run if the bus stop met at 10:15 am.?

Result

t = 5:45

#### Solution:

$27=3^3 \ \\ 30=2 \cdot 3 \cdot 5 \ \\ LCM(27, 30)=2 \cdot 3^3 \cdot 5=270 \ \\ \ \\ m=LCM(27,30)=270 \ \\ t=10+15/60-m/60=10+15/60-270/60=\dfrac{ 23 }{ 4 }=5.75=5:45$

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