Let X be the number. From the above properties of X, one can see that, "X+1" is a multiple of the numbers from 2 to 10. As Bonanova is asking for the smallest number with such properties, "X+1" must be the LCM (least common multiple) of the numbers from 2 to 10 -- which is 2520. And hence, X = 2520-1 = 2519.