Why is the while loop not working, python [closed]

The question is probably stupid, but I can't catch the error in my thoughts. I need to find the least common multiple. I know algorithms for solving this problem, but I wanted to experiment:

a = int(input())
b = int(input())

if a > b:
    i = a
    while i % a != 0 and i % b != 0 and i < a * b:
        i += 1
    print(i)   
else:
    i = b
    while i % a != 0 and i % b != 0 and i < a * b:
        i += 1
    print(i)

However, the numbers I enter do not go through the while loop, i is output as I assigned it.

Help, please, to understand where I am stupid.

source https://stackoverflow.com/questions/74923498/why-is-the-while-loop-not-working-python

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