smc

To find the largest number of "repeated" crates necessary, we must account for all the possibilities of the number of apples in each crate. Since each crate contains a minimum of $120$ apples and a maximum of $144$ apples, there are $144-120+1=25$ different amounts possible for the number of apples per crate. Now, we have to count for the worst case scenario: the $25$ amounts are repeated as many times as possible. $25$ can go into $128$ exactly $5$ times because $5\cdot 25=125$, which is less than $128$. This leaves a remainder of $3$ crates. The worst case scenario would be that these $3$ crates have a different number of apples each. It doesn't actually matter how many apples are in these $3$ crates because any of the $25$ values would be repeated again anyway. So, the answer is $5+1=\boxed{6}$