# Count integers in the range [A, B] that are not divisible by C and D

Given four integers A, B, C and D. The task is to find the count of integers in the range [A, B] that are not divisible by C and D .

Examples:

Input: A = 4, B = 9, C = 2, D = 3
Output: 2
5 and 7 are such integers.

Input: A = 10, B = 50, C = 4, D = 6
Output: 28

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

Approach: First include all the integers in the range in the required answer i.e. B – A + 1. Then remove all the numbers which are divisible by C and D and finally add all the numbers which are divisible by both C and D.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the count of ` `// integers from the range [a, b] that ` `// are not divisible by c and d ` `int` `countNums(``int` `a, ``int` `b, ``int` `c, ``int` `d) ` `{ ` `    ``// Numbers which are divisible by c ` `    ``int` `x = b / c - (a - 1) / c; ` ` `  `    ``// Numbers which are divisible by d ` `    ``int` `y = b / d - (a - 1) / d; ` ` `  `    ``// Find lowest common factor of c and d ` `    ``int` `k = (c * d) / __gcd(c, d); ` ` `  `    ``// Numbers which are divisible by both c and d ` `    ``int` `z = b / k - (a - 1) / k; ` ` `  `    ``// Return the required answer ` `    ``return` `b - a + 1 - x - y + z; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a = 10, b = 50, c = 4, d = 6; ` ` `  `    ``cout << countNums(a, b, c, d); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG ` `{ ` ` `  `// Function to return the count of ` `// integers from the range [a, b] that ` `// are not divisible by c and d ` `static` `int` `countNums(``int` `a, ``int` `b, ``int` `c, ``int` `d) ` `{ ` `    ``// Numbers which are divisible by c ` `    ``int` `x = b / c - (a - ``1``) / c; ` ` `  `    ``// Numbers which are divisible by d ` `    ``int` `y = b / d - (a - ``1``) / d; ` ` `  `    ``// Find lowest common factor of c and d ` `    ``int` `k = (c * d) / __gcd(c, d); ` ` `  `    ``// Numbers which are divisible by both c and d ` `    ``int` `z = b / k - (a - ``1``) / k; ` ` `  `    ``// Return the required answer ` `    ``return` `b - a + ``1` `- x - y + z; ` `} ` `static` `int` `__gcd(``int` `a, ``int` `b)  ` `{  ` `    ``if` `(b == ``0``)  ` `        ``return` `a;  ` `    ``return` `__gcd(b, a % b);      ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String []args)  ` `{ ` `    ``int` `a = ``10``, b = ``50``, c = ``4``, d = ``6``; ` ` `  `    ``System.out.println(countNums(a, b, c, d)); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python3 implementation of the approach ` `from` `math ``import` `gcd ` ` `  `# Function to return the count of  ` `# integers from the range [a, b] that  ` `# are not divisible by c and d  ` `def` `countNums(a, b, c, d) : ` ` `  `    ``# Numbers which are divisible by c  ` `    ``x ``=` `b ``/``/` `c ``-` `(a ``-` `1``) ``/``/` `c;  ` ` `  `    ``# Numbers which are divisible by d  ` `    ``y ``=` `b ``/``/` `d ``-` `(a ``-` `1``) ``/``/` `d;  ` ` `  `    ``# Find lowest common factor of c and d  ` `    ``k ``=` `(c ``*` `d) ``/``/` `gcd(c, d);  ` ` `  `    ``# Numbers which are divisible  ` `    ``# by both c and d  ` `    ``z ``=` `b ``/``/` `k ``-` `(a ``-` `1``) ``/``/` `k;  ` ` `  `    ``# Return the required answer  ` `    ``return` `(b ``-` `a ``+` `1` `-` `x ``-` `y ``+` `z);  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``a ``=` `10``; b ``=` `50``; c ``=` `4``; d ``=` `6``;  ` ` `  `    ``print``(countNums(a, b, c, d));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `     `  `class` `GFG ` `{ ` ` `  `// Function to return the count of ` `// integers from the range [a, b] that ` `// are not divisible by c and d ` `static` `int` `countNums(``int` `a, ``int` `b, ``int` `c, ``int` `d) ` `{ ` `    ``// Numbers which are divisible by c ` `    ``int` `x = b / c - (a - 1) / c; ` ` `  `    ``// Numbers which are divisible by d ` `    ``int` `y = b / d - (a - 1) / d; ` ` `  `    ``// Find lowest common factor of c and d ` `    ``int` `k = (c * d) / __gcd(c, d); ` ` `  `    ``// Numbers which are divisible by both c and d ` `    ``int` `z = b / k - (a - 1) / k; ` ` `  `    ``// Return the required answer ` `    ``return` `b - a + 1 - x - y + z; ` `} ` ` `  `static` `int` `__gcd(``int` `a, ``int` `b)  ` `{  ` `    ``if` `(b == 0)  ` `        ``return` `a;  ` `    ``return` `__gcd(b, a % b);      ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String []args)  ` `{ ` `    ``int` `a = 10, b = 50, c = 4, d = 6; ` ` `  `    ``Console.WriteLine(countNums(a, b, c, d)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```28
```

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