程序找到三个数字的公比

给定a：b和b：c。任务是编写一个程序来查找比率a：b：c
例子：

Input: a:b = 2:3, b:c = 3:4
Output: 2:3:4

Input:  a:b = 3:4, b:c = 8:9
Output: 6:8:9

方法：技巧是使通用术语“ b”在两个比率中相等。因此，将第一比率乘以b ₂ (第二比率的b项)，然后将第二比率乘以b ₁ 。

Given: a:b₁ and b₂:c 
Solution: a:b:c = (a*b₂):(b₁*b₂):(c*b₁)
For example: 
If a : b = 5 : 9 and b : c = 7 : 4, then find a : b : c.
Solution: 
Here, Make the common term ‘b’ equal in both ratios. 
Therefore, multiply the first ratio by 7 and the second ratio by 9. 
So, a : b = 35 : 63 and b : c = 63 : 36 
Thus, a : b : c = 35 : 63 : 36

下面是上述方法的实现：

C++

// C++ implementation of above approach
#include 
using namespace std;
 
// Function to print a:b:c
void solveProportion(int a, int b1, int b2, int c)
{
    int A = a * b2;
    int B = b1 * b2;
    int C = b1 * c;
 
    // To print the given proportion
    // in simplest form.
    int gcd = __gcd(__gcd(A, B), C);
 
    cout << A / gcd << ":"
         << B / gcd << ":"
         << C / gcd;
}
 
// Driver code
int main()
{
 
    // Get the ratios
    int a, b1, b2, c;
 
    // Get ratio a:b1
    a = 3;
    b1 = 4;
 
    // Get ratio b2:c
    b2 = 8;
    c = 9;
 
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
 
    return 0;
}

Java

// Java implementation of above approach
 
import java.util.*;
import java.lang.*;
import java.io.*;
class GFG{
 
static int __gcd(int a,int b){
    return b==0 ? a : __gcd(b, a%b);
}   
 
// Function to print a:b:c
static void solveProportion(int a, int b1, int b2, int c)
{
    int A = a * b2;
    int B = b1 * b2;
    int C = b1 * c;
  
    // To print the given proportion
    // in simplest form.
    int gcd = __gcd(__gcd(A, B), C);
  
    System.out.print( A / gcd + ":"
         + B / gcd + ":"
         + C / gcd);
}
  
// Driver code
public static void  main(String args[])
{
  
    // Get the ratios
    int a, b1, b2, c;
  
    // Get ratio a:b1
    a = 3;
    b1 = 4;
  
    // Get ratio b2:c
    b2 = 8;
    c = 9;
  
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
}
}

Python 3

# Python 3 implementation
# of above approach
import math
 
# Function to print a:b:c
def solveProportion(a, b1, b2, c):
 
    A = a * b2
    B = b1 * b2
    C = b1 * c
 
    # To print the given proportion
    # in simplest form.
    gcd1 = math.gcd(math.gcd(A, B), C)
 
    print( str(A // gcd1) + ":" +
           str(B // gcd1) + ":" +
           str(C // gcd1))
 
# Driver code
if __name__ == "__main__":
 
    # Get ratio a:b1
    a = 3
    b1 = 4
 
    # Get ratio b2:c
    b2 = 8
    c = 9
 
    # Find the ratio a:b:c
    solveProportion(a, b1, b2, c)
 
# This code is contributed
# by ChitraNayal

C#

// C# implementation of above approach
using System;
 
class GFG
{
static int __gcd(int a,int b)
{
    return b == 0 ? a : __gcd(b, a % b);
}
 
// Function to print a:b:c
static void solveProportion(int a, int b1,
                            int b2, int c)
{
    int A = a * b2;
    int B = b1 * b2;
    int C = b1 * c;
 
    // To print the given proportion
    // in simplest form.
    int gcd = __gcd(__gcd(A, B), C);
 
    Console.Write( A / gcd + ":" +
                   B / gcd + ":" +
                   C / gcd);
}
 
// Driver code
public static void Main()
{
 
    // Get the ratios
    int a, b1, b2, c;
 
    // Get ratio a:b1
    a = 3;
    b1 = 4;
 
    // Get ratio b2:c
    b2 = 8;
    c = 9;
 
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
}
}
 
// This code is contributed
// by Akanksha Rai(Abby_akku)

Javascript

    // Javascript implementation of above approach
     
    function __gcd(a, b)
    {
        return b == 0 ? a : __gcd(b, a % b);
    }
 
    // Function to print a:b:c
    function solveProportion(a, b1, b2, c)
    {
        let A = a * b2;
        let B = b1 * b2;
        let C = b1 * c;
 
        // To print the given proportion
        // in simplest form.
        let gcd = __gcd(__gcd(A, B), C);
 
        document.write( A / gcd + ":" + B / gcd + ":" + C / gcd);
    }
 
    // Get the ratios
    let a, b1, b2, c;
   
    // Get ratio a:b1
    a = 3;
    b1 = 4;
   
    // Get ratio b2:c
    b2 = 8;
    c = 9;
   
    // Find the ratio a:b:c
    solveProportion(a, b1, b2, c);
     
    // This code is contributed by divyeshrabadiya07.

输出：

6:8:9