Later, King led a famous march on Washington and worked for equal rights.

--------------
(Is this sentence correct? The use of the preposition 'on'?)

Usually, we'd use the preposition "to" in a sentence like this, but for this particular march, the preposition "on" has always been used. I think this is because he was leading such a large group of people, and because they were not going there for pleasure. They had a definite purpose.