My idea is this (Im asking to either confirm this or skip it)
Jews and xians have the same god. That should not be any doubt I guess. Xians recognize Jesus as the mesiah but the father of jesus is the god that the jews worship.
Muslims does not recognize jesus as the mesiah (help me out here) but instead se mohamad as the prophet. Mohamad based his ideas (besides from Gods word) on the OT.
In the quran we can therefore se shortversions of the OT here and there. We can see the stories or Abraham, Noah, Adam & Eve, Moses etc. The same God.
It OT testament was written sometimes 2000 - 1000 BC, NT should have been written down around 300 AD and the quran should have been written in pretty close to 600 AD. All in the same region.
When worshipping the very same God. Whats the problem?