I need to determine the number of elements in Z_25 direct product with Z_5.

i know that i need to count the elements with property that (lcm(|a|,|b|))= 5

and then break in to the cases that |a|=|b| = 5. the other case will be...

But what i am missing is know how choices can there be for both and b.

My book says that when |a|=|b| = 5. there are 4 choices for a and four choices of b. i dont know why.

I need help coming up with the choices for a and b. i need to know how many and what are they.