Please help: Keyword question

I have two local keywords that are almost the same. In order to get them ranking better should I target just the one or will I have to link build for both in order to get them both to rank?

Keyword example (obviously fake):

Los Angeles Widgets
Los Angels CA widgets

The real keywords both currently rank #11.

I don't think it will make much difference since they are very similar and the second keyword contains the first one.

Aim for the shorter one. The longer one will come from LSI