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

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++

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// 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;
}

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Java

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// Java implementation of the above approach
import java.util.*;
import java.lang.*;
import java.io.*;
  
class GFG
{
  
// Recursive function to find 
// gcd using euclidean algorithm 
static 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 
static int lcm(int n, int m) 
    return (n * m) / gcd(n, m); 
  
// Driver code 
public static void main(String[] args) 
    int n = 2, m = 3, k = 5
  
    System.out.print( k / lcm(n, m));
}
  
// This code is contributed by mohit kumar 29

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Python3

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# Python3 implementation of the above approach 
  
# Recursive function to find 
# gcd using euclidean algorithm 
def gcd(a, b) : 
  
    if (a == 0) : 
        return b; 
          
    return gcd(b % a, a); 
  
# Function to find lcm 
# of two numbers using gcd 
def lcm(n, m) :
  
    return (n * m) // gcd(n, m); 
  
  
# Driver code 
if __name__ == "__main__"
  
    n = 2; m = 3; k = 5
  
    print(k // lcm(n, m)); 
  
# This code is contributed by AnkitRai01

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Output:

0

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



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Improved By : AnkitRai01, mohit kumar 29