What is the smallest number greater than 1 that, when divided by 2, 3, 4, 5 or 6 leaves a remainder of 1 in each case?

How do get 61 as the answer?

Elkville High won a Friday night b-ball game by 10 points; the next night they scored 25 points more than on Friday and again won by 10 points. The sum of the opponents' scores for the 2 games was 109. How many points did Elkville score on Friday?

Again, how do you get 52 as the answer?

If 537^102 were calculated, it would have 279 digits. What would the digit farthest to the right be (the ones digit)?

Why is the answer 9??

And lastly, what is the smallest possible value for the product of two real numbers that differ by 6?

The answer is -9 but why??