Let's try to answer this in plain and simple fashions. The above question, "does LHC have the potentiality to destroy earth?" - I can only assume that this question is posted in a direct line of thought that was really based as: "Can LHC create a black hole, and, in doing so, destroy the earth?"
The short answer is NO. The only anser is NO. There is, in fact, a truely very distinct, very real possibility for creating said black hole in the operational runs of LHC. Is this going to destroy the world which we love and cherish so? Never. The power reels that would be required for such would be to the point of ridicule. The real answer lies inside basic astro-physics. The truth is that a black hole, upon it's creation, is a relative proportion of the mass which, in dying or destruction, created it. Everything about a black hole, it's definition, size, and, yes, earth-gobbling suction, is based on the technique which bore it.
So, let's have a quick look here at the facts-
1. if a black hole were to be created with sub-atomic particles, said black hole also would be sub-atomic, unless engineered to become otherwise.
2. the design, the purpose of a black hole is to regain the lost mass which has been replaced after destruction with anitmatter forces, stronger than the most powerful force we know of, the speed of light.
3. the lost mass required in order to "fill" a black hole is an inverted ratio of its original mass, the newly added antimass, and, if needed in the equation, the forces, if irregular or external, of the destruction of said matter in the first place.
4. black holes CANNOT exist anywhere inside an atmosphere- there is simply too much to gobble up and "fill" itself in any atmosphere for one to exist only breifly.
In summation, said potential black hole created by LHC would likely be no more than maybe %20 larger than the protons fired and would be extremely capable of withdrawing any matter necessary to "fill" that %120. Truth be told, it would likely die so quickly that we probably wouldn't even be capable of measuring it. I think that the more likely scenario of LHC destroying the Earth would be related to if the coolant systems all failed simultaneously, gassed up, then exploded, and, if by chance LHC was built along a series of fault lines on the earth's crust maybe, in a very sci-fi kind of way, it could cause enough damage to create worldwide lava eruptions. Imagine the odds of that?