A Core method

# a core method determine start/end dates of prior months 
  use strict; use warnings; 
  use Time::Local;

  my @startend; # [0] is current noncompleted month others are full mo
+nths back
                # in each of those the sub elements are
                #   [0] yyyy mm 
                #   [1] is start yyyy mm dd 
                #   [2] is end yyyy mm dd 

  my $date; 
  my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) =localtime(
+time) ; 
  # move to noon so DST  changes dont kill ya 
  my $now_fix12=timelocal( 0, 0, 12, $mday, $mon, $year);
  $date=$now_fix12; 

  my $back=24; 
  for my $m (0..$back) {push @startend,['']}; 

  my $todo=0; 
  my $doing;
  my ($ym,$ymd); 

  $doing=$startend[$todo]; 
  ($date,$ym,$ymd)=getparts($date); 
  startup($doing,$ym,$ymd); 
  while (1) { 
    ($date,$ym,$ymd)=getparts($date); 
#    print $ymd."\n";
    unless ($doing->[0] eq $ym) { 
      $todo++; 
      last if ($todo>$back); 
      $doing=$startend[$todo]; 
      startup($doing,$ym,$ymd); 
      } 
    else {$doing->[1]=$ymd; } 
  } # while 

for my $doing (@startend) {
   print join(' | ',@$doing)."\n"; 
   } 
exit; 

sub startup {
  my $doing=shift; 
  my $ym=shift; 
  my $ymd=shift; 
  $doing->[0]=$ym; 
  $doing->[1]=$ymd; 
  $doing->[2]=$ymd; 
  } # startup  

sub getparts { 
  my $date=shift; 
  my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) =localtime(
+$date) ; 
  my $ymd=sprintf('%4d %02d %02d',$year+1900,$mon+1,$mday); 
  my $ym=substr($ymd,0,7); 
  $date=$date-24*60*60;   
  return ($date,$ym,$ymd); 
  }
[download]

Result

2017 06 | 2017 06 01 | 2017 06 23
2017 05 | 2017 05 01 | 2017 05 31
2017 04 | 2017 04 01 | 2017 04 30
2017 03 | 2017 03 01 | 2017 03 31
2017 02 | 2017 02 01 | 2017 02 28
2017 01 | 2017 01 01 | 2017 01 31
2016 12 | 2016 12 01 | 2016 12 31
2016 11 | 2016 11 01 | 2016 11 30
2016 10 | 2016 10 01 | 2016 10 31
2016 09 | 2016 09 01 | 2016 09 30
2016 08 | 2016 08 01 | 2016 08 31
2016 07 | 2016 07 01 | 2016 07 31
2016 06 | 2016 06 01 | 2016 06 30
2016 05 | 2016 05 01 | 2016 05 31
2016 04 | 2016 04 01 | 2016 04 30
2016 03 | 2016 03 01 | 2016 03 31
2016 02 | 2016 02 01 | 2016 02 29
2016 01 | 2016 01 01 | 2016 01 31
2015 12 | 2015 12 01 | 2015 12 31
2015 11 | 2015 11 01 | 2015 11 30
2015 10 | 2015 10 01 | 2015 10 31
2015 09 | 2015 09 01 | 2015 09 30
2015 08 | 2015 08 01 | 2015 08 31
2015 07 | 2015 07 01 | 2015 07 31
2015 06 | 2015 06 01 | 2015 06 30
[download]

Note that element 0 in @startup is the current non completed month, others are full months back

If you are just dealing with days, $date=$date-24*60*60; is fine if $date starts at noon.