Firstly, 271 is a prime number, secondly to satisfy the condition you need to find M = 271 x a, choose smallest value of 'a' such that 2010 must be divisible by 'a' and 'a' must be greater than 271.gcd(M, 2010) > gcd(M, 271) > 1.

Find all possible values for gcd(M, 2010).

Eg. M = 271 x 335 = 90785

gcd(90785,271) = 271

gcd(90785,2010) = 335

335 > 271 > 1