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

Software Development
#1

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)))