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)))