Should we use G.C.D or L.C.M?

$5958,5814,5430$ leave same remainder when x divides them,
Therefore $5958-5814=144$ is divisible by $x$ . $5814-5430=384$ is divisible by $x$ . $5958-5430=528$ is divisible by $x$ .
Therefore the largest possible value of $x$ which will divide the given numbers is the $H.C.F$ of $144,384,528=\boxed {48}.$