How to make this linear time complexity to log time complexity?-CodePudding

I was practising for a coding challenge and I got stuck up with this problem.

A and his friend bought a number each from the integer shop, A has number N and his friend has number M. A wants that both their numbers should be co-primes. To achieve this, A divides both the numbers by the largest number which can divide both the numbers. A wants to know the sum of numbers after doing this operation, help him find that sum.

Input

Input: 
N = 6, M = 5
Output: 
11
Explanation:
The largest number that can divide both 
5 and 6 is 1. 
After dividing, 5 6 = 11.

I have tried this code

long sum(long N, long M){
    long divider = 1;
    long min = Math.min(N,M);
    for(long i=2; i<=min; i  )
        if(N%i==0 && M%i==0)
            divider=i;
    return (N/divider)   (M/divider);
}

But the expected run-time complexity is O(log(n)). But my code gives O(n).

I'm not able to find any method to make it logarithmic. Please any help me.