Note: This is how I clean my dishwasher, but I'm clearly not a professional dishwasher cleaner. To the contrary, I'm a crazy woman mixing up homemade cleaning products in her kitchen while the children nap. I'm probably going to blow myself up some day. All this to say that you should read your dishwasher's manual and be careful and use common sense, etc etc.
Step 1: Remove the bottom rack and any visible food debris in the bottom of the dishwasher.
Step 2: Remover the filter(s). This is the cage thingy that catches your food bits. My dishwasher has two. Removing them will involve removing some screws or bolts. Be careful once you remove the filter not to drop the screws (or anything else, for that matter) down the now uncovered drain hole.
The underside of these filters are likely mighty gross. Clean the filters in a sink full of warm water and vinegar. Wear rubber gloves. And a haz-mat suit. Just kidding. Sort of.
Step 3: Use a wet vac to remove all the water and debris in the bottom of your dishwasher and down the drain hole (If you don't own a wet vac, you can just sop it up with paper towel and clean it by hand).
Step 4: Fill a spray bottle with vinegar and spray any stuck on sediment or visible dirt. Also clean the inside bottom lip just below the door. That seems to be a place where ickyness thrives.
Step 5: Screw filters back in place.
Step 6: Use tweezers to remove any debris that may be clogging up the spray holes in the spinning arm.
Step 7: Use Q-tips to clean the hot air vent. I read once that the hot air vent normally comes right off, so I tried desperately to pull mine off with a butter knife. The moral of that story is that not all of them are meant to come off. So unless you are sure that yours is removable, just clean it with some Q-tips right where she is.
Step 8: Clean door edges and gasket with vinegar or your favorite mild cleaning solution.
Step 9: If there are rust stains in your dishwasher you can clean them quite easily by combining baking soda with hydrogen peroxide to make a paste. Apply the paste with a sponge and then remove it with a cloth. You'll want to be wearing rubber gloves, especially if your skin is sensitive. It is shocking how easily this solution lifts the rust stain.
I like to give my dishwasher a good clean a couple times a year. If I was in the habit of rinsing my dishes it would be less often, but lets face it...that's just not going to happen.
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