This is the 130th most frequent Swedish word.
minst
"Minst" means "least" or "at least" in English.
In this sentence, 'minst' is used to indicate the minimum amount of time it can take, suggesting it could take longer.
Det tar minst två timmar att köra till staden.
It takes at least two hours to drive to the city.
Here, 'minst' is used to compare sizes and indicates that he is the smallest or youngest.
Han är minst av alla syskonen.
He is the smallest of all the siblings.
In this context, 'minsta' is a form of 'minst' signifying even the smallest contribution can be helpful.