import math
from decimal import Decimal

def largest_common_power_of_10(numbers):
    return Decimal(math.gcd(*numbers)).normalize().as_tuple().exponent

print(largest_common_power_of_10([1234, 5000, 200]))
print(largest_common_power_of_10([470_363_000, 143_539_000, 1_200_000]))
print(largest_common_power_of_10([11_230_000, 1_540_000, 44_500_000]))