Re: How can the Kaioken times three exist?
Kaio-ken is just the name of the technique. We see from the fight with Freeza that he actually doesn't have to call anything out.
I personally believe that he shouts it as a focusing technique, to clarify mentally how strong he's going to be. Remember that at this time the Kaio-Ken was pretty damn new to him, and so I think when he started to realise he might need to go beyond simply doubling his strength, he subdivided the name further to help him focus on it. As far as I'm concerned, Kaio-Ken alone simply relates to any of them, from x2 to x20.
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