gemeinsamen
Gemeinsam is a German adjective meaning joint, shared, or common. The form gemeinsamen is one declined form of this adjective and appears when it directly precedes a noun that is declined in certain cases, most notably in the dative and in plural with a definite determiner. In practice, gemeinsamen is common in phrases describing collective actions or characteristics.
Examples illustrate its use. mit gemeinsamen Zielen means with shared goals (dative plural). dem gemeinsamen Projekt
Etymology traces gemeinsam back to the adjective gemein, meaning common, with the suffix -sam forming an adjective
Usage notes: gemein’s basic function is as an attributive adjective; as an adverb, the form does not