in order to help sb / sth or because you like sb / sth; in order to get or keep sth
for the sake of sb / sth
in order to help sb / sth or because you like sb / sth
They stayed together for the sake of the children.
for the sake of sth / of doing sth
in order to get or keep sth
The translation sacrifices naturalness for the sake of accuracy.
Definitions from the Oxford Advanced Learner's Dictionary, 9th edition