last minute vs minute

last minute and minute both are nouns.

Word	Noun	Adjective	Verb	Adverb
last minute	Yes	No	No	No
minute	Yes	Yes	No	No

As nouns, minute is a hypernym of last minute; that is, minute is a word with a broader meaning than last minute:

Other hypernyms of last minute include instant, moment, second.

last minute (noun)	minute (noun)
the latest possible moment	distance measured by the time taken to cover it
	a short note
	a unit of angular distance equal to a 60th of a degree
	a unit of time equal to 60 seconds or 1/60th of an hour
	an indefinitely short time
	a particular point in time

last minute (adjective)	minute (adjective)
	characterized by painstaking care and detailed examination
	infinitely or immeasurably small