This is the 846th most frequent Serbian word.
великим
"Великим" means "great" or "big" (instrumental singular form of "велики" in Serbian).
In this sentence, 'великим' is used as an instrumental plural adjective modifying the noun 'брзинама' (speeds).
Путовали смо великим брзинама.
We traveled at great speeds.
Here, 'великим' acts as an instrumental singular adjective describing the noun 'бројем' (number).
Разговарао је са великим бројем људи.
He spoke with a large number of people.
In this case, 'великом' is a locative singular adjective qualifying the noun 'граду' (city).