Can you use one toothbrush on multiple cats if you rinse it out well?

I have three cats and I want to get a pet dental care system, which comes with one toothbrush and toothpaste so I wanted to know if it was ok to use one toothbrush on my three cats if I rinse it out well every time.
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I'm sure it's fine as long as none of your cats are sick. But make sure you wash it (a dishwasher could probably clean it well) before you use it on another cat.
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