Are there any cheap and easy ways of cleaning spent cartridge cases?

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I do a bit of reloading to save money on ammo, and the only problem with that is that spent brass gets a bit grotty. I can't afford to buy a case tumbler at the moment, so I've been looking for cheap and easy improvised ways to clean the cartridge cases. The best I've come up with so far is to tie a bunch of cases into the sleeve of an old shirt and stick them in the washing machine. It gets the cases visibly cleaner, but it's not perfect and I'm concerned that if I do that too much I'll end up damaging the machine. Does anyone know of any really cheap and simple ways to clean brass?