Problem of the Week Problem E Three Lists

Ameya has two lists, List $$1$$ and List $$2$$, which each have six entries that are consecutive positive integers. The smallest entry in List $$1$$ is $$a$$ and the smallest entry in List $$2$$ is $$b$$, and $$a < b$$.

Ameya creates a third list, List $$3$$. The thirty-six entries in List $$3$$ come from the product of each number in List $$1$$ with each number of List $$2$$. (There could be repeated numbers in List $$3$$.)

Suppose that List $$3$$ has $$49$$ as an entry, has no entry that is multiple of $$64$$, and has an entry larger than $$75$$. Determine all possible pairs $$(a, b)$$.