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Nothing. As ppl have said, there isn't like a min frequency. A digital design can work at as low freq as possible.
But if the system is producing a real time output , say such as mp3 decoding or video decoding, then there has to be a min freq, below which your throughput will fall to less then what is needed, and the output will no longer a video/audio you require.for example your video may become a slow-motion
Hope it helps,