Program to find LCM and HCF of two numbers without using Loops in C

Hi Friends,
          In the previous blogpost you have seen that I have implemented the LCM and HCF using loops. Now I'm here to find out LCM and HCF without loops in which we will use recursion.

         To implement it , I will use Euclidean algorithm. 

In mathematics, the Euclidean algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements.  -Wikipedia

Algorithm :
function gcd(a, b)
    if b = 0
       return a; 
       return gcd(b, a mod b);

HCF : I will calculate HCF using Eulidean algorithm.

LCM : As we know that if we know the HCF of any two numbers we can easily find out LCM by using below formula.

      LCM = (Number1 * Number2) / HCF

I have used 70 and 90 in my last blogspot example. I'm going to use same numbers here.

HCF = 10 (Calculated by Algorithm).

LCM = (70 * 90 ) / 10 = 630.

Let's write the program.

     Program to implement LCM , HCF using Euclidean Algorithm.
     Created By : Pirate

int hcf(int a,int b);
int lcm(int a,int b);
int main(){
    int number_a,number_b;
    printf("Enter the two no\n");
    printf("\nHighest Common Factor HCF is %d\n", hcf(number_a,number_b));
    printf("\nLowest Common Multiple LCM is %d", lcm(number_a,number_b));
    return 0;
int hcf(int a, int b){
        return b;
int lcm(int a,int b){
    int temp;
    temp = hcf(a,b);
    return (a * b) / temp;


Output :

Enjoy :)


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