Program to find the common ratio of three numbers

Given a:b and b:c. The task is to write a program to find ratio a:b:c
Examples: 

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

Learn About : Ratio and Proportions

Approach: The trick is to make the common term ‘b’ equal in both ratios. Therefore, multiply the first ratio by b₂ (b term of second ratio) and the second ratio by b₁.

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

Below is the implementation of the above approach: 

// C++ implementation of above approach
#include <bits/stdc++.h>
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 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 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# 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)

<script>
    // 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.
</script>

<?php
// PHP 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)
{
    $A = $a * $b2;
    $B = $b1 * $b2;
    $C = $b1 * $c;

    // To print the given proportion
    // in simplest form.
    $gcd = __gcd(__gcd($A, $B), $C);

    echo ($A / $gcd) . ":" . 
         ($B / $gcd) . ":" . ($C / $gcd);
}

// Driver code

// Get the ratios
// 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 mits
?>

6:8:9

Time Complexity : O(log(A+B)) ,where A=a*b2 and B = b1*b2

Space Complexity : O(1), since no extra space has been taken.