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.
**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
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++ implementation of the above approach
// Recursive function to find
// gcd using euclidean algorithm
(a == 0)
gcd(b % a, a);
// Function to find lcm
// of two numbers using gcd
(n * m) / gcd(n, m);
// Driver code
n = 2, m = 3, k = 5;
cout << k / lcm(n, m) << endl;
Time Complexity : O(log(min(n,m)))