((current date) - (day (current date)) day)

SQL> SELECT To_char(To_date('01/' 
                       ||Substr(To_char(SYSDATE, 'MM/YYYY'), 1, 7), 'DD/MM/YYYY' 
               ) - 1, 
              'YYYY-MM-DD') LAST_DAY 
FROM   dual   2    3    4    5  
  6  ;

LAST_DAY
----------
2015-05-31

LAST_DAY(ADD_MONTHS(SYSDATE,-1))

TRUNC(SYSDATE, 'MM')

SQL> SELECT SYSDATE, TRUNC(SYSDATE, 'MM') -1 LAST_DAY_PREV_MNTH FROM dual;

SYSDATE   LAST_DAY_
--------- ---------
15-JUN-15 31-MAY-15

SQL> SELECT SYSDATE, LAST_DAY(ADD_MONTHS(SYSDATE,-1)) LAST_DAY_PREV_MNTH FROM dual;

SYSDATE   LAST_DAY_
--------- ---------
15-JUN-15 31-MAY-15

SQL>

SQL> select sysdate "NOW", trunc(sysdate,'MONTH')-1 "PREV_LAST_DAY" from dual;
NOW                 PREV_LAST_DAY
------------------- -------------------
15/06/2015 07:05:46 31/05/2015 00:00:00