This is the 11832nd most frequent Russian word.
замке
"Замке" means "lock" (in the prepositional case) or "castle" depending on context.
In this sentence, 'замке' is used to refer to 'lock,' and it is in the prepositional case as part of the phrase 'на замке' to indicate the state of the door being locked.
Дверь была заперта на замке.
The door was locked with a lock.
Here, 'замке' refers to 'castle' and is in the prepositional case, indicating the location where the tours took place.
Во старом замке проводились экскурсии.
Tours were conducted in the old castle.
In this context, 'замке' again refers to 'lock,' and is in the prepositional case, describing the location where the key was hidden.