Each remainder is one less than the divisor so if we take the LCM of the numbers between 2 and 9 and subtract 1 we should find the lowest number that satisfies the requirement.
Because 2 and 4 are factors of 8, we can ignore them; similarly we ignore 3 because it divides into 9. That leaves us with 5, 6, 7, 8, 9.
The LCM of 6 and 9 is 18, and the LCM OF 18 and 8 is 72. The LCM is therefore 5×7×72=2520. So the number we want is 2519.