Chose a number between 55 and 101 that is a multiple of 3,6, and 7

Use prime factorization.

3 = 3
6 = 3 × 2
7 = 7

So the lowest common factor is 2*3*7 (drop the other 3 because it's a duplicate) which is equal to 42. Any multiple of that will be a multiple of 3, 6, and 7.

So all we need is a multiple of 42 which is between 55 and 101, which would be 84.