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Much cheaper than Lemi Shine is just plain citric acid, which I also use. I find it at our local 'Sharp Shopper' and also in a Menoite store in the valley at Denton VA just south of Harrisburg. Looks for all the world like old fashion washing detergent before they started putting all that stuff in it.

Why? Well several reasons but the main one is it will clean better than tumbling, INCLUDING the INSIDE, and PRIMER POCKETS. Good enough for me, and cheap to boot. A small fan dries the brass on a tray while laying on a towel. Then a quick polish --
After doing this for some time I located and bought a first NRA reloading manual that at one point talked about using citric acid to clean brass. By then, for once, I was ahead of the curve.

We are talking, at the time, of cleaning, after depriming, several 41/2 gallon buckets of brass.