Problem 2. The distance between telephone poles on a street 1600 m long was 80 m. Due to the planting of new trees on the street, the poles were relocated so that the new distance between the poles is 50 m. How many poles remained in the same place after the relocation?
Solution. Since $\operatorname{LCM}(50,80)=400$, and the first pole remains in its place, we get that the total number of poles that are not moved is $1+1600: 400=1+4=5$ poles.