The minimum number of testcases cannot be counted directly. Only based on requirements, we can calculate the minimum number of test cases.

Using SRS-->Functional requirements-->Function point analysis will be done, based on that, testers can do test point analysis-->based on that no.of.test cases can be calculated.Remember it is only one of the way, other ways are also practiced.

EMC is one of the methods, EMC stands for Easy Medium and Complex functionalities, we can roughly allocate,

easy functionality--> x no.of test cases ;

medium functionality-->y no.of. functionality

and

complex functionality-->z no.of. functionality,

so the no.of. test cases can be

Total no.of. test cases = {X * no.of.easy functionalities} + {Y * no.of.medium functionalities} + {Z * no.of.complex functionalities}