jmc

The prime factorizations of these integers are $154=2\cdot 7\cdot 11$ and $252=2^2\cdot 3^2\cdot 7$. The prime factorization of their greatest common divisor (GCD) must include all of the primes that their factorizations have in common, taken as many times as both factorizations allow. Thus, the greatest common divisor is $2\cdot 7=\boxed{14}$.