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 \((a, b)\).