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*on one's way (to some place)
leaving one place for another; en route to a place. (*Typically: be ~; get ~.) I have to leave. I am on my way to the bank. I will be there soon. I'm on my way now.
on one's way
(to something or some place) Go to on the way (to something or some place).
on your way
leaving or away Give me a kiss and I'll be on my way. They stayed with us for a week and then went on their way.