Find the file-name of the most recent Full Database Backup for a SQL Server database

Find-MostRecentFullBackup.ps1

function Find-MostRecentFullBackup([string]$ServerInstance, $database="master"){
#$db = "Adventureworks"

$rs = Invoke-Sqlcmd -ServerInstance $ServerInstance -Database msdb -Query "
WITH LatestBackupSet (database_name, BackupsAgo, backup_start_date, media_set_id)
AS
(
SELECT database_name
            , ROW_NUMBER() OVER (PARTITION BY database_name ORDER BY backup_start_date DESC) AS 'BackupsAgo'
            , backup_start_date
            , media_set_id
  FROM msdb.dbo.backupset bs
WHERE type != 'L'
)
SELECT bf.physical_device_name, lbs.* 
  FROM dbo.backupmediafamily bf
  JOIN LatestBackupSet lbs
    ON lbs.media_set_id = bf.media_set_id
   AND lbs.BackupsAgo = 1
   AND family_sequence_number = 1
   AND lbs.database_name = '$database'
"

$rs.physical_device_name
}