this should work if you have gnu date:
1 day ago <month> 1
<month>
here is current month, for example
kent$ date -d'1 day ago may 1'
Tue Apr 30 00:00:00 CEST 2013
another example, find the last day of the month before July:
kent$ date -d'1 day ago july 1'
Sun Jun 30 00:00:00 CEST 2013
note that, the timestamp was set to 00:00:00
.
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