slight discrepancy between size reported by df and lvs commands

Issue

Even being careful to select identical units, there is some difference between lvs and df :

# df /dev/mapper/VG01-Root
Filesystem           1K-blocks      Used Available Use% Mounted on
/dev/mapper/VG01-Root 
                      12709344   9755412   2319828  81% /
# lvs --units k /dev/mapper/VG01-Root
  LV   VG   Attr      LSize        Pool Origin Data%  Move Log Cpy%Sync Convert
  Root VG01 -wi-ao--- 12910592.00k

Both output above are shown in KiB (1024 bytes)

# lvs --units K /dev/mapper/VG01-Root
  LV   VG   Attr      LSize        Pool Origin Data%  Move Log Cpy%Sync Convert
  Root VG01 -wi-ao--- 13220446.21K
# df -B KB /dev/mapper/VG01-Root
Filesystem          1kB-blocks      Used Available Use% Mounted on
/dev/mapper/VG01-Root
                     13014369kB 9989542kB 2375504kB  81% /

Trying the same using 1KB == 1000 bytes, we still see a discrepancy in the size of the file system : the lvs command always reports bigger size.