What is "greatest common denominator"

Denominator \De*nom"i*na`tor\, n. [Cf. F. d['e]nominateur.]

1. One who, or that which, gives a name; origin or source of a name.

   This opinion that Aram . . . was the father and denomination of the Syrians in general.
   --Sir W. Raleigh.

2. (Arith.) That number placed below the line in common fractions which shows into how many parts the integer or unit is divided.

   Note: Thus, in 3/5, 5 is the denominator, showing that the integer is divided into five parts; and the numerator, 3, shows how many parts are taken.

3. (Alg.) That part of any expression under a fractional form which is situated below the horizontal line signifying division.

   Note: In this sense, the denominator is not necessarily a number, but may be any expression, either positive or negative, real or imaginary.
   --Davies & Peck (Math. Dict.)

   common denominator a number which can divide either of two or more other numbers without leaving a remainder in any of the divisions; as, 2 and 4 are common denominators of 12 and 28..

   greatest common denominator the largest common denominator of two or more numbers; as, 9 is the greatest common denominator of 18 and 27..