Number Theory

The Greatest Common Divisor has to be either 1 or 7. 

If the GCD is 7, there are 12 options form: $7,14,21,28,35,42,49,56,63,70,84,98$ (Note: it can't be 77 or 91, because both are factors of 1001)

If the GCD is 1, m must be a number without the factors 7, 11, or 13.

There are $100-(14+9+7-2) = 72$ numbers that meet these criteria

Thus, the answer is $72+12=\color{brown}\boxed{84}$