the most common language in the eastern mediterranean during the height of the roman empire was
Koine Greek.
Languages of the Roman Empire
Koine Greek had become a shared language around the eastern Mediterranean and diplomatic communications in the East, even beyond the borders of the Empire. 
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Languages of the Roman Empire [SEP] Introduction
Koine Greek had become a shared language around the eastern Mediterranean and diplomatic communications in the East, even beyond the borders of the Empire. The international use of Greek was one condition that enabled the spread of Christianity, as indicated for example by the choice of Greek as the language of the New Testament in the Bible and its use for the ecumenical councils of the Christian Roman Empire rather than Latin. With the dissolution of the Empire in the West, Greek became the dominant language of the Roman Empire in the East, modernly referred to as the Byzantine Empire.