Correct but you could also say travel for business. I prefer on though.

We might say 'travel on business' or 'travel for business' or 'I'm here on business', but we would only usually say 'for leisure'.

Hi, Carolina I think for both phrases you would use ‘for’ instead of ‘on’. In other words, “travel for business” and “travel for leisure”. I hope this helps 😊✨