I was able to find the Greatest Common Divisor of two numbers by using the Euclidean Algorithm. But what is the easiest way to express this GCD as a linear combination in the form c=au+bv where c is the GCD of a,b?

For example, the gcd(56,72)=8. And the linear combination can be expressed as 8 = (56)4-(72)(3). What's the easiest way to actually find this combination without simply guessing?