Horrendous Horror.

You happen to visit a school. You meet the maths teacher of the school and ask her for the total number of enrollments in the past \(20-25\) years. The maths teacher doesn't know what exactly it is but quite evasively leaves you with a puzzle that she's sure that you can never solve. The puzzle is as follows: To have an equal number of students in a classroom, they tried grouping them in a size of \(71,73,75,77\) students. To their irritation, they found that \(12,26,34,59\) students are left in each case. She then asks you to find the least number of enrollments with which such a scenario is possible. Will you outsmart her??

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