Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE table_name_27 ( league_cup INTEGER, total VARCHAR, championship VARCHAR, fa_cup VARCHAR )

### Question ###
Championship larger than 3, and a FA Cup smaller than 3, and a Total smaller than 6 involves what highest league cup?

### Accurate SQL ###

SELECT MAX(league_cup) FROM table_name_27 WHERE championship > 3 AND fa_cup < 3 AND total < 6