This is the 5257th most frequent Russian word.
общими
"Shared," "common," or "general" (instrumental plural form).
In this sentence, "общими" (common) is used as an adjective agreeing with "усилиями" (efforts), indicating a quality of being mutual or shared.
Мы обсудили это с общими усилиями.
We discussed this with combined efforts.
Here, "общими" (common) modifies "интересами" (interests), emphasizing that the interests are shared among the participants.
Проблема была решена на основе общими интересами.
The issue was resolved based on common interests.
In this case, "общими" (broad/general) modifies "словами" (words) to suggest a general description rather than a detailed one.