C program to implement Euclid’ s algorithm

Problem

Implement Euclid’ s algorithm to find the greatest common divisor (GCD) and least common multiple (LCM) of two integers and to output the results along with the given integers.

Solution

The solution to implement Euclid’ s algorithm to find the greatest common divisor (GCD) and least common multiple (LCM) of two integers is as follows −

The logic used to find GCD and LCM is as follows −

if(firstno*secondno!=0){
   gcd=gcd_rec(firstno,secondno);
   printf("\nThe GCD of %d and %d is %d\n",firstno,secondno,gcd);
   printf("\nThe LCM of %d and %d is %d\n",firstno,secondno,(firstno*secondno)/gcd);
}

The called function is as follows −

int gcd_rec(int x, int y){
   if (y == 0)
      return x;
   return gcd_rec(y, x % y);
}

Program

Following is the C program to implement Euclid’ s algorithm to find the greatest common divisor (GCD) and least common multiple (LCM) of two integers −

#include<stdio.h>
int gcd_rec(int,int);
void main(){
   int firstno,secondno,gcd;
   printf("Enter the two no.s to find GCD and LCM:");
   scanf("%d%d",&firstno,&secondno);
   if(firstno*secondno!=0){
      gcd=gcd_rec(firstno,secondno);
      printf("\nThe GCD of %d and %d is %d\n",firstno,secondno,gcd);
      printf("\nThe LCM of %d and %d is %d\n",firstno,secondno,(firstno*secondno)/gcd);
   }
   else
      printf("One of the entered no. is zero:Quitting\n");
   }
   /*Function for Euclid's Procedure*/
   int gcd_rec(int x, int y){
   if (y == 0)
      return x;
   return gcd_rec(y, x % y);
}

Output

When the above program is executed, it produces the following result −

Enter the two no.s to find GCD and LCM:4 8

The GCD of 4 and 8 is 4

The LCM of 4 and 8 is 8