This is the 12797th most frequent Russian word.
крупнейшими
"Крупнейшими" means "the largest" or "the biggest" (instrumental plural form).
The word 'крупнейшими' is used as an instrumental plural adjective to describe the cities being the largest.
Москва и Санкт-Петербург являются крупнейшими городами России.
Moscow and Saint Petersburg are the largest cities in Russia.
Here, 'крупнейшими' is used as an instrumental plural adjective to describe the companies being the largest in the market.
Эта организация сотрудничает с крупнейшими компаниями мирового рынка.
This organization collaborates with the largest companies of the global market.
In this sentence, 'крупнейшими' is an instrumental plural adjective, describing the achievements as being the greatest.