LSH and minhasing - Why does hashing the signature matrix make sense?

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I'm learning about LSH and minhashing and I'm trying to understand the rational of hashing the signature matrix:

We divide the signature matrix to bands and we hash (using which hash function?) every portion of column to k buckets. Why would it make sense? If we use a regular hash function then even a slight difference in two columns would probably lead to different buckets.

I do understand the relation between the signature matrix to Jacard distance but I don't understand the next step which is essentially hashing that distributes items evenly.

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