stoichiometry - More than one way of balancing a chemical equation

My textbook had this question on balancing chemical reactions

Ozone reacts with nitric oxide to give nitrogen dioxide and oxygen gas

Here's how I balanced it: $$\ce{O3 + NO -> NO2 + O2}$$

However I realised that the equation is also balanced if I write it as: $$\ce{2O3 + 4NO -> 4NO2 + O2}$$

and when it is written as: $$\ce{3O3 + NO -> NO2 + 4O2}$$

This seems wrong as I am sure that there cannot be more than one way of balancing a reaction but I do not have a satisfactory explanation. What is going wrong here?