最小正方形可均匀切割矩形

给定一个矩形板，长度为l，宽度为w。我们需要将此工作表划分为正方形工作表，以使正方形工作表的数量尽可能少。

例子：

Input :l= 4 w=6
Output :6
We can form squares with side of 1 unit, But the number of squares will be 24, this is not minimum. If we make square with side of 2, then we have 6 squares. and this is our required answer.
And also we can’t make square with side 3, if we select 3 as square side, then whole sheet can’t be converted into suares of equal length.

Input :l=3 w=5
Output :15

正方形边的最佳长度等于两个数字的GCD

C++

// CPP program to find minimum number of
// squares to make a given rectangle.
#include 
using namespace std;
  
int countRectangles(int l, int w)
{
    // if we take gcd(l, w), this
    // will be largest possible
    // side for suare, hence minimum
    // number of square.
    int squareSide = __gcd(l, w);
  
    // Number of squares.
    return (l * w) / (squareSide * squareSide);
}
  
// Driver code
int main()
{
    int l = 4, w = 6;
    cout << countRectangles(l, w) << endl;
    return 0;
}

Java

// Java program to find minimum number of
// squares to make a given rectangle.
  
class GFG{
static int __gcd(int a, int b) {
   if (b==0) return a;
   return __gcd(b,a%b);
}
static int countRectangles(int l, int w)
{
    // if we take gcd(l, w), this
    // will be largest possible
    // side for suare, hence minimum
    // number of square.
    int squareSide = __gcd(l, w);
  
    // Number of squares.
    return (l * w) / (squareSide * squareSide);
}
  
// Driver code
public static void main(String[] args)
{
    int l = 4, w = 6;
    System.out.println(countRectangles(l, w));
}
}
// This code is contributed by mits

Python3

# Python3 code to find minimum number of
# squares to make a given rectangle.
  
import math 
  
def countRectangles(l, w):
  
    # if we take gcd(l, w), this
    # will be largest possible
    # side for suare, hence minimum
    # number of square.
    squareSide = math.gcd(l,w)
      
    # Number of squares.
    return (l*w)/(squareSide*squareSide)
  
# Driver Code
          
if __name__ == '__main__':
    l = 4
    w = 6
    ans = countRectangles(l, w)
    print (int(ans))
  
# this code is contributed by
# SURENDRA_GANGWAR

C#

// C# program to find minimum number of
// squares to make a given rectangle.
  
class GFG{
static int __gcd(int a, int b) {
if (b==0) return a;
return __gcd(b,a%b);
}
static int countRectangles(int l, int w)
{
    // if we take gcd(l, w), this
    // will be largest possible
    // side for suare, hence minimum
    // number of square.
    int squareSide = __gcd(l, w);
  
    // Number of squares.
    return (l * w) / (squareSide * squareSide);
}
  
// Driver code
public static void Main()
{
    int l = 4, w = 6;
    System.Console.WriteLine(countRectangles(l, w));
}
}
// This code is contributed by mits

输出：

6