By the way my first attempt timed out on two test cases (whereas iampetermitsel's solution works). Can somebody help me, how is my solution different from his?

    min_b = b[0]
max_a = a[-1]

common_multiples_a = []
elem = max_a
while elem <= min_b:
    if all(elem % item == 0 for item in a):
        common_multiples_a.append(elem)
        elem += max_a

count = 0
for elem in common_multiples_a:
    if all(item % elem == 0 for item in b):
        count +=1

        return count