in order to help sb / sth or because you like sb / sth; because of the interest or value sth has, not because of the advantages it may bring
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 sth's sake
because of the interest or value sth has, not because of the advantages it may bring
I believe in education for its own sake.
Definiciones del Oxford Advanced Learner's Dictionary, 9.ª edición