find the least positive integer N so that 1<gcd(N, 271) < gcd(N, 2014). Explain how you find N.

Question

Thanks for your help

Answer 1

271 is prime, so N is a multiple of 271
2014 = 2*19*53,

If N = 271*2*2014, GCD(N,2014) = 2*271 and GCD(N,271) = 271

So, it appears to me that 271*2*2014 is the smallest N that fits the requirements