can you explain difference between if and elif in this code

I am trying to write a func. that finds LMC. But when i use if instead of elif, it becomes infite loop. But i didnt get why it happens. Can you explain me the logic?

def ekok(sayi,sayi1):
i = 2
b = 1
while(True):
        if (sayi % i == 0) and (sayi1 % i == 0) :
            b *= i
            sayi //= i
            sayi1 //= i
        elif (sayi % i == 0) and (sayi1 % i != 0):
            b *= i
            sayi //= i
        elif (sayi % i != 0) and (sayi1 % i == 0):
            b *= i
            sayi1 //= i
        else :
            i += 1
        if (sayi == 1) and (sayi1 == 1):
            break
return b