There are 2 train companies operating 2 routes - RE7, ICE 79. The cheapest train costs $44 and is 3h 27min.
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There are 4 ways to travel from DTM to LGG. 2 flights, 2 trains, 2 buses and 1 by car are possible between the two areas. The by car from DTM to LGG is the cheapest. The by car from DTM to LGG is the fastest. The train operated by running from Holzwickede to Bierset-Awans is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!