I have Two data frames

import pandas as pd
exam_1 = pd.DataFrame({'user': ['A', 'B', 'C'], 
                   'marks': [10, 50, 40]})

exam_2 = pd.DataFrame({'user': ['A', 'C', 'D'], 
                   'marks': [30, 20, 30]})

I’m trying to get a resultant data frame, with users appeared in both exams with lowest marks.
In the above example result should be:

          user   marks
           A      10
           C      30

I did write following lines to get users who appeared in both exams but, stuck in getting the lowest marks. Here is what I have tried

tmp = pd.merge(exam_1, exam_2, how='inner', on=['user'])
USERS = exam_1[ exam_1['user'].isin(tmp['user'])]

can someone please help me to get lowest exam marks in the resultant dataframe?