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**Product of integers with N and M digits**

N = 2, M = 3: 10 * 100 = 1000, D = 4 = [N + M - 1]

N = 2, M = 3: 99 * 100 = 9900, D = 4 = [N + M - 1]

N = 2, M = 3: 10 * 999 = 9990, D = 4 = [N + M - 1]

N = 2, M = 3: 99 * 999 = 98901, D = 5 = [N + M]

N = 2, M = 4: 10 * 1000 = 10000, D = 5 = [N + M - 1]

N = 2, M = 4: 99 * 1000 = 99000, D = 5 = [N + M - 1]

N = 2, M = 4: 10 * 9999 = 99990, D = 5 = [N + M - 1]

N = 2, M = 4: 99 * 9999 = 989901, D = 6 = [N + M]

Thus: the answer is N+M-1 and N+M.

Note:

3^4 = 81

3^5 = 243

3^6 = 729

3^7 = 2187

3^8 = 6561

Thus:

3^n = 1 if remainder(n/4) = 0

= 3 if remainder(n/4) = 1

= 9 if remainder(n/4) = 2

= 7 if remainder(n/4) = 3

Similarly, last digit of 4^n is 6 is n is an even number and 4 if n is an odd number.

Similarly, last digit of 7^n

Thus:

7^n = 1 if remainder(n/4) = 0

= 7 if remainder(n/4) = 1

= 9 if remainder(n/4) = 2

= 3 if remainder(n/4) = 3