Question

The least common multiple (lcm) of two positive integers u and v is the smallest positive integer that is evenly divisible by both u and v. Thus, the lcm of 15 and 10, written lcm (15,10), is 30 because 30 is the smallest integer divisible by both 15 and 10. Write a function lcm() that takes two integer arguments and returns their lcm. The lcm() functon should calculate the least common multiple by calling the gcd() function from program 7.6 in accordance with the following identity:

lcm (u, v) = uv / gcd (u, v)

u, v >= 0

(In C language)

hint: You will need to use the authors gcd function in an expression.

Program 7.6:

/* Function to find the greatest common divisor of two

     nonnegative integer values and to return the result    */

#include

int gcd (int u, int v)

{

            int temp;

            while (v != 0)

            {

                        temp = u % v;

                        u = v;

                        v = temp;

            }

            return u;

}

int main (void)

{

            int result;

            result = gcd (150, 35);

            printf ("The gcd of 150 and 35 is %i\n", result);

            result = gcd (1026, 405);

            printf ("The gcd of 1026 and 405 is %i\n", result);

            printf ("The gcd of 83 and 240 is %i\n", gcd (83, 240));

            return 0;

}