Pierre H.:
> "on a national and international scale"
> "on a national and an international scales"
The plural "scales" is wrong.  As to the article usage, I think
it's a matter of preference, and I prefer the second style here.
> And would it change if I used "both" before national?
> 
> "on both national and international scale"
> "on both a national and international scale"
You changed the options from the first example.  The new option with
no articles is also possible, but again, the one I prefer is with two
articles: "on both a national and an international scale".
-- 
Mark Brader            "'A matter of opinion'[?]  I have to say you are
Toronto                  right.  There['s] your opinion, which is wrong,
m...@vex.net              and mine, which is right."  -- Gene Ward Smith
My text in this article is in the public domain.