Hi Mike, and welcome to the forum.
I can't see the detail because it's not in focus, but your magazine is not contemporary to the pistol. The aluminum bottom magazines were introduced later, in the early 1930s through 1942, with the Russians/East Germans continuing them after WW-II.
You've got a nice looking Luger that looks to be in its original finish. Keep it that way! If you haven't cleaned and lubricated it, do it now and do it carefully. If you remove the grips, be particularly careful not to chip the left one near the safety lever.
If all the numbers on parts match (4 digits or the last 2 digits) consider not firing it, since breaking a part will considerably reduce it's historic value and interest to collectors - not that you're going to give up your Grandfather's Luger... Check to see if any of his papers can be found - if he received the normal authorization from his unit officer, you'll want to get his "bring back papers" that list this gun's serial number.
In this community, most members don't worry about making serial numbers known - in fact, this often helps some of the studies being done by collectors here.
DWM was the company that Georg Luger worked for when he developed the Parabellum Pistol. They made a good quality product, and your pistol has been part of three eras in Germany. With your Grandfather, you are literally holding history in your hand!
Marc
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 Igitur si vis pacem, para bellum -
- Therefore if you want peace, prepare for war.
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