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]))
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