A place to ask bicycle repair questions, and for bike shop monkeys to share advanced non commercial wrenching resources (no YouTube self promotion). This is only for repair related topics.
I assume you mean the easiest gear on the front and back, meaning the small chain ring up front and the large sprocket in the back.
Start with a new chain first. If you get a new cassette you'll also need a new chain anyways. A bike shop should be able to look at the drive train to see which part needs to be replaced.
@alvaro @bikewrench I don't think anything is necessarily wrong. The combination bends the chain to the greatest extent possible as it goes all the way left to all the way right, so it's going to be misaligned. Use another equivalent combo with less chain bending.