Similar to the above solution, you could also try an array formula. However, this will require you to do a MAX function on each sheet (preferably in the same cell on each sheet). For example, on sheet '1', you have MAX(B2:C2) in cell D1, and then the same on sheet '2', sheet '3', etc. Then on your summary sheet, use this array formula:
=MAX(N(INDIRECT(ADDRESS(1,4,,,ROW(INDIRECT("A1:A"&last_sheet))))))
Then be sure to hit Ctrl+Shift+Enter to enter it as an array formula.
This assumes "last_sheet" is some integer value like 6 for example, then makes a range string of it ("A1:A6"), passes this to INDIRECT which passes it to ROW() giving you an array from 1:6. This array is used as the list of sheet names for ADDRESS which creates an array of references at cell D1 on each of the six sheets. The array is passed to INDIRECT which returns #VALUE! errors until you pass the array of errors to N(). Finally, max returns the largest value in the array. You can use "Evaluate Formula" to see how it breaks down step by step, but hopefully this is a good starting point for you!