The following definitions are analogous to
those for integers.
Let R be a field and let a, b 
R[X].
Definitions
- A common divisor of a and b is a polynomial which divides both a and b.
- A common divisor d is called greatest common divisor (gcd) if, moreover, every common divisor of a, b (not both zero) is a divisor of d.
- A common multiple of a and b is a polynomial which is divisible by both a and b.
- A least common multiple (lcm) of a and b is a common multiple of a and b of minimal degree at least 0.
The concept gcd is only meaningful when the polynomials a, b
are not both equal to the zero polynomial.
Proposition
If c and d are two
greatest common divisors of the polynomials a, b (not
both the zero polynomial), then there is a constant q 
0 such that
qc = d.