Can I run D&D as a DM with the DMG and MM?

[BlueBlackRed]

There is no requirement what-so-ever for you to buy anything beyond the first 3 books to run a game.

Heck, if you learn certain things well enough you can put your modules on 2-4 sheets of paper and not need anything more.

 

[the Jester]

No problem at all.

The one thing I'd recommend is adding 1/2 level to monster damage; that's a shortcut, but it really makes them more meaningful, especially as the party goes up in levels.