What is the value of x:
(1) The lowest common multiple of x and 16 is 48.
The lowest common multiple is the smallest number that both terms will go into evenly. For x and 16, the lowest common multiple is 48. 16 factors to 2*2*2*2 and 48 factors to 2*2*2*2*3.
This means that x must include a single 3, when factored, and CAN include up to four 2's.
This means x can be 3, 6, 12, 24, or 48, and no other values. Since we don't have a single value for x, this statement is insufficient.
(2) The greatest common factor of x and 16 is 4.
This tells us that The largest number (or factor) that x and 16 have in common is 4.
This means that x must contain two 2's in its prime factorization. It cannot have MORE or LESS than two 2's, but it may have other numbers, like a 3 or a 5 or a 7, or any other prime number.
This means that x can be 4, 12, 20, etc., but it can NOT be 24, since that factors to 2*2*2*3, and this would make the GCF 8 instead of 4.
Again, we have multiple values possible for x, so this statement is insufficient.
Together, however, the only number that meets both conditions is 12, so C is our answer.