Say I have a number 2010. The divisors that I'm allowed to use is 2010, 670, 1005, 402, and 355.

Now it says there exists a number M, between 10020000 and 10030000 so that the number and 2010 share a gcd. I don't understand how to get the number besides guessing and checking. Also it seems like any multiple of the divisors will hit a number between that range. But the question insists there's one answer...

e.g. 2010 * 4990 = 10029900

1005 * 9975 = 10024875 which is within the range

Maybe I'm interpreting the question wrong...