# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// 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

 ` `

Output:

```6:8:9
```

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