This is the 2513th most frequent Korean word.
많다고
"많다고" means "is said to be many" or "is considered to be a lot."
In this sentence, '많다고' is used to report what someone heard about the quantity or extent of diverse cultures in Korea. It suggests indirect quotation.
한국에는 다양한 문화가 많다고 들었습니다.
I heard that there are many diverse cultures in Korea.
Here, '많다고' communicates the act of bragging about the number of friends one has, emphasizing indirect or reported speech.
친구들이 많다고 자랑했어요.
They bragged about having many friends.
In this case, '많다고' describes the state of the library being crowded, expressed through indirect knowledge or realization.