• This C Program calculates the GCD and LCM of two integers.

• Here GCD means Greatest Common Divisor. For two integers a and b, if there are any numbers d so that a / d and b / d doesn’t have any remainder.

• Such a number is called a common divisor.

• Common divisors exist for any pair of integers a and b, since we know that 1 always divides any integer.

• We also know that common divisors can’t get too big since divisors can’t be any larger than the number they are dividing.

• Hence a common divisor d of a and b must have d <= a and d <= b.

• Here, LCM means Least Common Multiplies. For two integer a & b, to know if there are any smallest numbers d so that d / a and d / b doesn't have a remainder.

• Such a number is called a Least Common Multiplier.

Program:

#include <stdio.h>
int main(){
    int num1, num2, gcd, lcm, remainder, numerator, denominator;
    printf("Enter two numbers:\n");
    scanf("%d %d", &num1, &num2);
    if (num1 > num2){
        numerator = num1;
        denominator = num2;
    }
    Else{
        numerator = num2;
        denominator = num1;
    }
    remainder = num1 % num2;
    while (remainder != 0){
        numerator   = denominator;
        denominator = remainder;
        remainder   = numerator % denominator;
    }
    gcd = denominator;
    lcm = num1 * num2 / gcd;
    printf("GCD of %d and %d = %d\n", num1, num2, gcd);
    printf("LCM of %d and %d = %d\n", num1, num2, lcm);
}

Output:

Enter two numbers: 24 36

GCD of 24 and 36: 24

LCM of 24 and 36: 36