I have a LG Dishwasher model LDS4821ST and when it goes into the cleaning mode it trips the gfi breaker.

Because they are garbage. They are to sensitive for the actual start up of an air conditioner. Take the gfi breaker out, when day of inspection put it in. Take it out when inspector leaves.

You may have a bad detergent dispenser.

LG lds4821 overheats filter board and burns it. Probably another part shorts and causes excessive current. Replacing the filter board makes dishwasher run but problem persists

Check the breaker carefully, it may have a GFI (Ground Fault Interrupter) built in. If it doesn't say anything about this on the breaker, look for a small 'test' button which is used to test the breaker's reaction to a fault condition. If it is GFI equipped, water has gotten into areas where it did not belong and is causing ground currents to flow activating the GFI.
If it is not so equipped, then the motor has probably failed drawing excessive current causing the breaker to trip.

Most dishwashers and other appliances using water, are protected by a Ground Fault Interrupter or GFI. These will sometimes trip without having detected any dangerous leakage current and others will get oversensitive causing them to trip well below their design current. A GFI wall socket will have two buttons on it; one to 'test' the other to reset. On some brands, when they are tripped, the reset button moves only a little further out and may not appear tripped. GFIs are also found combined with circuit breakers that also differ in appearance from the unprotected type and will also have a reset button. If your dishwasher is plugged in under the kitchen sink, check its appearance to see if it is GFI equipped.
BTW, these can be used in one location and connected so all of the wall plugs on the same circuit can be served by a single GFI equipped breaker so check any others nearby as well.
If a GFI refuses to stay set, it may be actually detecting some leakage current of a dangerous level so don't assume the GFI is bad, the appliance on it its circuit may have developed an internal problem.

Before looking into your built-in dishwasher as the problem, check your main electrical panel to see if you have tripped a circuit breaker. If not, you may have tripped a GFI receptacle located on or around your kitchen counter.  If so, reset it! Then try the dishwasher. However, if this IS the problem, this may become an ongoing problem. I agree with (and its code) having a GFI breaker in your kitchen.  But what I don't agree with is when the contractor/electrician who installed this, didn't take into consideration that when these GFI's are put in series with other receptacles (for added protection) in the kitchen, they trip more easily when plugged in with certain appliances because of the motors (eg. refrigerators, dishwashers, etc.) in them. The GFI's sole purpose is for protecting you around the sink where there's running water. It trips on milliamps so you won't get electrocuted around the sink. Also, if you have other appliances running at the same time the dishwasher's running, makes them more susceptible to trip. So in conclusion, first check for power. Second, check for GFI breaker (or vice versa). I believe you should find your problem here. If so, reset it and wait to see how and when this does it again. GFI breaker's are sensitive breakers. They tend to wear out before a regular outlet (receptacle) does. Not knowing how long and old this (GFI) receptacle is, I'd replace that if it happens more frequently. This usually does the trick. I hope it's not your built-in dishwasher. If so, feel free to contact me again, and I'll help you with that too. Good Luck with this, and I hope you get everything back in working order. Take care, Jim

Replace the GFCI, it may be defective. If that doesn't correct the problem, there may not be anything that you can do; GFCI monitors the current that passes from the hot to the neutral wire, and trips when the amperage is unbalanced. GFCI tripping may not indicate a problem with the machine

Probable cause is a single pole gfi opposed to a double pole gfi.
* Do not use a single pole GFCI ON A MULTI WIRE CIRCUIT, IT WILL NUISANCE TRIP IMMEDIATELY
Use a two pole GFCI circuit breaker on such circuits.

WASHING MACHINES ARE NOT TO BE CONNECTED TO GFI OUTLETS AND TRY TO CONNECT IT TO A CERCIUT THAT IS NOT WITH YOUR DRYER. (REG) OUTLET.

DISHWASHER SHOULD NOT BE ON A GFI CERCIUT. THATS YOUR PROBLEM . SHOULD BE A DEDICATED CERCIUT BUT IF NOT JUST INSTALL A REG OUTLET DONT WORRY THE DISHWASHER WILL TRIP THE BREAKER IN YOUR PANEL IF THERE IS A SHORT WITH THE WATER.