The sentence lavo los platos en la lavadora means I wash the plates in the washing machine. So lavadora translates into washing machine. Thus, it's illogical that you wash the plates in this machine because we use the dishwasher for this purpose. So dishwasher means lavavajillas. Finally, the correct sentence is:
<em>Lavo los platos en </em><em>el lavavajillas</em>
