You are always limited by the IC's max frequency!But you are still limited by the maximum IC fv. Higher than its maximum and you are in the same situation as I am.
it is just that can vary from sub-MHz (e.g. 4000B series CMOS at lower voltages) to many GHz in the case of GaAs pre-scaler ICs.
Btw, what is he maximum fv it can see this 74LS93 ? Actually I will check it as well.
The LS93 has two divider, the first is a single stage, the 2nd a 3-stage counter. Typically you clock the first and use its output to clock the 2nd for max dividing ratio.
A check in the data sheet shows this:
Also they show the logic for the LS90 (BCD = 10) and LS92 (divide 12).