The kitchen faucet is the original piece when the house was built, have been fixed a couple of times over the course of its service, and it is getting more frequent, last time was about a year ago, I believe the water corrosion is causing the grommet and ring rubbers to wear faster, it cannot be shut completely and with slow dripping. Moen has life time warranty on its products, I requested parts and got them pretty soon by mail.
First, took off the Moen brand plate covering the handle screw access, unscrew it and take off the handle, thread off the cap, then took off the plastic position lock and assembly lock. Then the lever was exposed.
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Unscrew and take out the lever, there is a pin that helps to lock in and center the cartridge, needed to be taken out to unlock the cartridge.
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The cartridge was ready to be extracted from the faucet stem, however, it might be stuck, thread the lever screw in to provide a grip to pull the cartridge out. Then push the center piece out from the cartridge, replace all the grommets and rings, put on silicon grease to all those rubber parts.
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Reverse the process to put everything back in, don't tighten the last screw to test cold and hot water, found it was switched, hit by 50% chance, back everything out, turned the cartridge 180 degree, and now turn everything back in nice and tight. Dripping stopped. Done.