Compute 189 × 214 (mod 15) by reducing first, then multiplying, then reducing again Reduce first, and then multiply (and reduce again) to compute 189 × 214 (mod 15).
So I somewhat understand modular arithmetic but was just looking for clarification and confirmation.
I divided 189 by 15 and got a remainder of 9 so I have 189 = 9(mod 15) and I divided 214 by 15 and got a remainder of 4 so I have 214 = 4(mod 15). Then I multiplied the remainders (9 x 4 = 36) and then divided 15 by 36 to get the final least residue/ remainder of 6. 
So the final answer I came up with is 189 x 214 = 6(mod 15).
Is my methodology correct and is that the most I can reduce? (I concluded that the least residue of 189 x 214 is 6 (mod 15). 

The steps are correct, and so is the end result. It sounds like just what the question was asking for.
${\style{font-family:inherit}{\tiny\text{( Posted as CW, just so that the question is taken off the "unanswered" list. )}}}$
