Sum of differences between products and LCMs

Question

I've been trying to solve this Codewars problem https://www.codewars.com/kata/56e56756404bb1c950000992

In this kata you need to create a function that takes a 2D array/list of non-negative integer pairs and returns the sum of all the "saving" that you can have getting the LCM of each couple of number compared to their simple product.

without importing any extra Python library/module.

My code passes al tests but it gets the "Execution Timed Out (12000 ms)" How can I solve this?

Thanks a lot in advance.

Here's my code:

def sum_differences_between_products_and_LCMs(pairs):

    result = 0

    # calculating LCM 
    for x, y in pairs:
        if x > y:
            greater = x
        else:
            greater = y

        while(True):
            if x == 0 or y == 0:
                lcm = 0
                break
            else:
                if((greater % x == 0) and (greater % y == 0)):
                    lcm = greater
                    break
            greater += 1

        result += ((x*y) - lcm)
    return result

Answer 1

I finally solved it with the following code (I basically decide to split the arguments of the formula into variables to calculate the LCM):

def sum_differences_between_products_and_LCMs(pairs):
    
    if pairs:

        gcd = [] #variable for the gcd
        for x, y in pairs:
            while(y):
                x, y = y, x % y
            gcd.append(x)

        prod = [] #variable for the product
        for x, y in pairs:
            prod.append(x * y)

        lcm = [] #variable for the lcm
        for p in range(len(prod)):
            if gcd[p] == 0:
                lcm.append(0)
            else:
                lcm.append(int(prod[p] / gcd[p]))

        result = 0
        for i in range(len(lcm)):
            result += (prod[i] - lcm[i]) # answering the problem question


        return result
    return 0 # if pairs is empty, return 0