Minimum wage vs poverty?

Does poverty need an increase in the minimum wage to address it?

How does the income on the minimum wage compare with the poverty line?

For the moment, let’s set aside the economic debate over whether the minimum wage costs jobs. (The CBO, majority of economists, and majority of empirical studies pretty much say it all.)
Instead, let’s address Sanders and Warren's moral argument for hiking the minimum wage to such levels: that “no one who works full time should have to live in poverty.” 

Also, links to evidence that mitigates against the "cherry picked data" argument.