I'm having trouble with the Chinese remainder theorem and i have several homework problems, could some one please help me out with one so I can know how to do the rest?

a) Find an integer having remainders 1, 2, 5, 5, when divided by 2, 3, 6, 12, respectively.

b) Find an integer having remainders 2, 3, 4, 5, when divided by 3, 4, 5, 6, respectively.

c) Find an integer having remainders 3, 11, 15, when divided by 10, 13, 17, respectively.

Thanks!