Hey mlane,
(1) factors of 30: 1, 2, 3, 5, 6, 10, 15, so K can be 3, 5 or 6. Please remind that when GMAT asks for a value, it should be one specific value. So INSUFF
(2) factors of 12: 1, 2, 3, 6, so K can be 3 or 6 and again INSUFF
(1+2) k can be either 3 or 6 so INSUFF.
Now, what if the propositions were:
(1) k is a prime factor of 30
(2) k is a prime factor of 12
Then the answer would be C like your pick.
Hope it helps.