Euclidean algorithm of number theory (i.)

Introduction:
Euclidean algorithm, also known as the greatest common divisor method, is the algorithm to solve the problem.

theorem:
The theoretical support for Euclid's algorithm is gcd recursive theorem, which is described below.
gcd recursive theorem:
For any nonnegative integer A and any positive integer B,GCD (A, b) = gcd (b, A%b)

Code:
From the above theorem, we can directly derive the code of the GCD function:

int gcd(int a,int b){    return b==0?a:gcd(b,a%b);}

Extensions:
According to the greatest common divisor of a, B, we can obtain a B least common multiple.
LCM functions:

int lcm(int a,int b){    return a/gcd(a,b)*b;}

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Euclidean algorithm of number theory (i.)