# Count common elements in two arrays containing multiples of N and M

Hello Everyone,

Given two arrays such that the first array contains multiples of an integer n which are less than or equal to k and similarly, the second array contains multiples of an integer m which are less than or equal to k.
The task is to find the number of common elements between the arrays.
Examples:

**Input :**n=2 m=3 k=9
Output : 1
First array would be = [ 2, 4, 6, 8 ]
Second array would be = [ 3, 6, 9 ]
6 is the only common element
**Input :**n=1 m=2 k=5
Output : 2

Approach :
Find the LCM of n and m .As LCM is the least common multiple of n and m, all the multiples of LCM would be common in both the arrays. The number of multiples of LCM which are less than or equal to k would be equal to k/(LCM(m, n)).
To find the LCM first calculate the GCD of two numbers using the Euclidean algorithm and lcm of n, m is n*m/gcd(n, m).
Below is the implementation of the above approach:

• C++
• Java
• Python3
• C#
• Javascript

`// C++ implementation of the above approach`

`#include <bits/stdc++.h>`

`using` `namespace` `std;`

`// Recursive function to find`

`// gcd using euclidean algorithm`

`int` `gcd(` `int` `a, ` `int` `b)`

`{`

` ` `if` `(a == 0)`

` ` `return` `b;`

` ` `return` `gcd(b % a, a);`

`}`

`// Function to find lcm`

`// of two numbers using gcd`

`int` `lcm(` `int` `n, ` `int` `m)`

`{`

` ` `return` `(n * m) / gcd(n, m);`

`}`

`// Driver code`

`int` `main()`

`{`

` ` `int` `n = 2, m = 3, k = 5;`

` ` `cout << k / lcm(n, m) << endl;`

` ` `return` `0;`

`}`

Output:

0

Time Complexity : O(log(min(n,m)))