Tram lines

Trams of five lines driven at intervals of 5,8,10,12 and 15 minutes. At 12 o'clock come out of the station at the same time. About how many hours again all meet? How many times have earch tram pass for this stop?

Result

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

Solution:

5 ... primenumber 8=23 10=25 12=223 15=35 LCM(5,8,10,12,15)=2335=120  m=LCM(5,8,10,12,15)=120 t=m/60=120/60=2 h5 \ ... \ 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}
a=m/5=120/5=24a=m/5=120/5=24
b=m/8=120/8=15b=m/8=120/8=15
c=m/10=120/10=12c=m/10=120/10=12
d=m/12=120/12=10d=m/12=120/12=10
e=m/15=120/15=8e=m/15=120/15=8



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