Transform multiple categorical columns

Here is one way

df.stack().astype('category').cat.codes.unstack()
Out[190]: 
   col1  col2
0     3     0
1     0     3
2     2     1
3     0     1

Or

s=df.stack()
s[:]=s.factorize()[0]
s.unstack()
Out[196]: 
   col1  col2
0     0     1
1     1     0
2     2     3
3     1     3

You can fit the LabelEncoder() with the unique values in your dataframe first and then transform.

le = LabelEncoder()
le.fit(pd.concat([df.col1, df.col2]).unique()) # or np.unique(df.values.reshape(-1,1))

df.apply(le.transform)
Out[28]: 
   col1  col2
0     3     0
1     0     3
2     2     1
3     0     1