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_48869 ( "Season" real, "Total Attendance" real, "Games" real, "Average" real, "High avg." real, "Team" text, "No. Of Clubs" real )

### Question ###
What is the smallest average for Beijing Guo'an when they played more than 240 games?

### Accurate SQL ###

SELECT MIN("Average") FROM table_48869 WHERE "Team" = 'beijing guo''an' AND "Games" > '240'