Below query can be used to check last full, differential and transaction log backup times in SQL Server.

SELECT sd.[Name] AS DatabaseName,
LastFullBackUpTime=(SELECT MAX(bs.backup_finish_date) FROM msdb.dbo.backupset bs WHERE
bs.[database_name]=sd.[name] AND bs.[type]='D'),
LastDiffBackUpTime=(SELECT MAX(bs.backup_finish_date) FROM msdb.dbo.backupset bs WHERE
bs.[database_name]=sd.[name] AND bs.[type]='I'),
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