Graduate schools require 2-3 letters of recommendation. Asking for a letter from busy proffesors is a big request, and there are a lot of factors to consider.

• Ask professors who you have maintained a relationship with. Consider asking professors who you have done research with and who you worked with closely in class. You want to ask professors who can speak about who you are as a student and how you will excel in graduate school.
• GIVE PROFESSORS TIME! Make sure you ask at least a month before they are due. Professors are doing you a favor. You want a good letter, so allow them the time to do so.
• Write them a thank you card for their time. This appreciation and gratitude goes a long way.

This article also provides excellent details on how to (and how not to) ask for letters of recommendation.
https://www.psichi.org/page/203EyeSpr16cGomez#.VyewkaMrJ0t