This is the 2194th most frequent Japanese word.
済む
"済む" means "to finish," "to end," or "to be completed."
Here, 済む is used to mean 'being completed' or 'to be finished'.
問題が簡単だったので、早く済みました。
Since the problem was simple, I finished it quickly.
Here, 済む is used to indicate 'to manage with something' or 'to be resolved with less (effort).'
この方法を使えば、手間が少なく済む。
If you use this method, you can complete it with less effort.
Here, 済む implies 'to be resolved' or 'to be settled.'