The 3524 switch and 3640 router both have switching power supplies. The 3524 is rated for 100-127V or 200-240V and the 3640 is rated for 100-240V, which means they will autoadjust to some extent for varying voltage levels. The main intent is for the same power supply to be able to work in differing regions where the voltage standard may be 110V or 220V, but they will also accept some up-and-down variance in voltage.
To answer your question, the power supplies are rated to run at a minimum of 100V. Below that, they will not be able to guarantee consistent DC output levels. So, 100 volts AC would be your answer.
If you intend to run your 3524 or 3640 with DC power supplies, the situation is more complex. The URLs below document some of the requirements.
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