Is it appropriate to ask for more than one recommendation letter from the same person I will be applying for Ph.D programs in mathematics and hence I'll be needing letters of recommendation from my professors. There are two or three professors with whom I have a lot of academic interaction and which are also famous in their research areas. As such, having a recommendation letter from them can significantly increase my chances of selection.

Now my question is: Since I’ll be applying to 5–6 universities, is it appropriate to ask for that many recommendation letters from the same person? If not, then how many recommendation letter is considered to be “normal number” to ask for? 

I would be very happy if some of the professors here, who themselves write recommendation letters can tell their experience.
Is there some reason to think that the professors will need to write different letters of recommendation for the different universities?  If not, then the additional incremental effort of sending the same letter to several different places is minimal.  Though I am not a professor, my role is similar, and I, at least, do not mind when somebody wants me to send the same letter to a handful of different locations.  If you were applying to 20 places, that might be a different matter...