# 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```

Approach: The trick is to make the common term â€˜bâ€™ 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 â€˜bâ€™ 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++

 `// 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)`

## PHP

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## Javascript

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Output:

`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.

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