GCD Function>>>

Greatest common divisor of two numbers is highest number smaller than or equal to minimum of two numbers which divides both numbers.
Algo would be like:
 a,b<=10^5
          for(int i=1;i<=min(a,b);i++)
                 {     if((a%i==0)&& (b%i==0))
                                  gcd=i;   }

More optimized algo given by euclid algorithm:
a,b<=10^9
Recursive definition:
int gcd(int a,int b)
{
if(b==0)
     return a;
else
      gcd(b,a%b);
}

Even more optimized algo for very long numbers 
a,b<=10^200
Calling Function: gcd(a,mod(str,a));

int mod(char str[],int d)
{
    int r=0,i;
    for(i=0;str[i];i++)
    {
        r=10*r+(str[i]-'0');
        r=r%d;
    }
    return r;
}
int gcd(int a,int b)
{
    if(b==0)
        return a;
    else
        gcd(b,a%b);
}

So Any gcd could be find out using above mentioned algos according to situations


Findng out lcm using gcd function

lcm(a,b)*gcd(a,b)=a*b;