We do not count zero as a common multiple. If we did, then zero would be the least common multiple of any two numbers (unless we also 

counted negative multiples, in which case there would be no least common multiple of any two numbers).

Either we make an exception in this case, so that the LCM of zero and any number is zero, or we make no exception, in which case the LCM of 

zero and any number does not exist. To me it makes more sense to say that the LCM is defined only for positive numbers.