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
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:
-
The program starts with the
mainfunction. -
It declares four integer variables:
x,y,m, andn. -
It uses
scanfto read two integers from the input and assigns them toxandy. -
It assigns the values of
xandytomandnrespectively. -
It enters a while loop that continues until
mandnare 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. -
Inside the loop, it checks if
mis greater thann. If it is, it subtractsnfromm. Otherwise, it subtractsmfromn. -
Once the loop finishes (when
mandnare equal), it prints the value ofn(orm, since they're equal), which is the GCD ofxandy.
As for the other operations you've mentioned:
-
To calculate
x + yusing repeated subtraction, you would need to repeatedly subtract 1 fromyand add 1 toxuntilybecomes 0. The result would bex, which is equal to the originalx + y. -
To calculate
x mod yusing repeated subtraction, you would need to repeatedly subtractyfromxuntilxbecomes less thany. The result would bex, which is equal to the originalx mod y. -
To calculate the least common multiple (LCM) of
xandy, you can use the formulaLCM(x, y) = (x * y) / GCD(x, y). You already have the GCD from the provided code, so you just need to multiplyxandyand divide the result by the GCD.
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