The common denominator is usually the Lowest (or Least) Common Multiple of the numbers involved. Where two numbers have no common factors then the LCM is simply the product of those numbers. As 19 is a Prime number and has no factors in common with 18 then the common denominator is 18 x 19 = 342.
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There can be no greatest common denominator. If you have a set a numbers whose least common denominator is L then 2*L, 3*L, … are all common denominators. There is no end to that sequence and so no greatest.
If 13 and 518 are both denominators, the LCD is 6734 If that's 1/3 and 5/18, the LCD is 18 and you can change 1/3 to 6/18
The Least Common Multiple (LCM) for 13 18 25 is 5,850.