How to find GCD, LCM on a set of numbers

I've used Euclid's algorithm to find the greatest common divisor of two numbers; it can be iterated to obtain the GCD of a larger set of numbers.

private static long gcd(long a, long b)
{
    while (b > 0)
    {
        long temp = b;
        b = a % b; // % is remainder
        a = temp;
    }
    return a;
}

private static long gcd(long[] input)
{
    long result = input[0];
    for(int i = 1; i < input.length; i++) result = gcd(result, input[i]);
    return result;
}

Least common multiple is a little trickier, but probably the best approach is reduction by the GCD, which can be similarly iterated:

private static long lcm(long a, long b)
{
    return a * (b / gcd(a, b));
}

private static long lcm(long[] input)
{
    long result = input[0];
    for(int i = 1; i < input.length; i++) result = lcm(result, input[i]);
    return result;
}

There is an Euclid's algorithm for GCD,

public int GCF(int a, int b) {
    if (b == 0) return a;
    else return (GCF (b, a % b));
}

By the way, a and b should be greater or equal 0, and LCM = |ab| / GCF(a, b)

There are no build in function for it. You can find the GCD of two numbers using Euclid's algorithm.

For a set of number

GCD(a_1,a_2,a_3,...,a_n) = GCD( GCD(a_1, a_2), a_3, a_4,..., a_n )

Apply it recursively.

Same for LCM:

LCM(a,b) = a * b / GCD(a,b)
LCM(a_1,a_2,a_3,...,a_n) = LCM( LCM(a_1, a_2), a_3, a_4,..., a_n )