prove that a( a + 1 )(2a + 1) is divisible by 6 for every integer a.

Now my book says

"By taking least absolute residues mod (6), we see that a = 0, -1,1 -2,2 or 3"

What the hell does "least absolute residue" mean? Can someone explain this very carefully? (Yes I'm self learning so please don't leave out any important details)

And how do they get a = 0,-1,1,-2,2 or 3???????

Thanks very much!!!