Thermocouple Calibration

If I have a standard K type thermocouple, how accurate are they? I have thermocouples that came with my multimeter, and my multimeter will read it with a certain level of accuracy, but if I pop a different thermocouple in there, how far off would it be?

Are most DMMs with thermcouples calibrated to the thermocouple they come with?

There are tables which show a thermocouple's accuracy, which BTW, is not constant across all of its range.
Acording to the Omega manual, in standard grade couples you can expect inaccuracies up to 2.2C at temepratures centered around 25C

To this, you would have to add the errors of the DMM's accuracy itself.