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int main(){int x, y, m, n;scanf ("%d %d", &x, &y);/* x > 0 and y > 0 */m = x; n = y;while (m != n){if(m>n)m = m - n;elsen = n - m;}printf("%d", n);}      x + y using repeated subtraction     x mod y using repeated subtraction      the greatest common divisor of x and y     the least common multiple of x and y

Question

int main(){int x, y, m, n;scanf ("%d %d", &x, &y);/* x > 0 and y > 0 */m = x; n = y;while (m != n){if(m>n)m = m - n;elsen = n - m;}printf("%d", n);}      x + y using repeated subtraction     x mod y using repeated subtraction      the greatest common divisor of x and y     the least common multiple of x and y

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Solution

The code you've provided is written in C language. It calculates the greatest common divisor (GCD) of two numbers x and y using the Euclidean algorithm. Here's a step-by-step explanation:

  1. The program starts with the main function.

  2. It declares four integer variables: x, y, m, and n.

  3. It uses scanf to read two integers from the input and assigns them to x and y.

  4. It assigns the values of x and y to m and n respectively.

  5. It enters a while loop that continues until m and n are equal. This is the main part of the Euclidean algorithm. The algorithm works by repeatedly subtracting the smaller number from the larger one until the two numbers become equal. That number then is the GCD of the original two numbers.

  6. Inside the loop, it checks if m is greater than n. If it is, it subtracts n from m. Otherwise, it subtracts m from n.

  7. Once the loop finishes (when m and n are equal), it prints the value of n (or m, since they're equal), which is the GCD of x and y.

As for the other operations you've mentioned:

  • To calculate x + y using repeated subtraction, you would need to repeatedly subtract 1 from y and add 1 to x until y becomes 0. The result would be x, which is equal to the original x + y.

  • To calculate x mod y using repeated subtraction, you would need to repeatedly subtract y from x until x becomes less than y. The result would be x, which is equal to the original x mod y.

  • To calculate the least common multiple (LCM) of x and y, you can use the formula LCM(x, y) = (x * y) / GCD(x, y). You already have the GCD from the provided code, so you just need to multiply x and y and divide the result by the GCD.

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