Replacing Lightroom 6 with Lightroom CC

I purchased a copy of stand-alone LR 6 when it was released but I have since joined up to a CC photography subscription covering LR CC and Photoshop CC.

Adobe Creative Cloud installed Photoshop CC ok, but it did not overwrite LR 6 with LR CC. The Creative Cloud treats LR 6 as though its an up to date copy of LR CC.

My question is how to force the swap over to LR CC, and get its new features?

I suspect that I could run an uninstall on LR 6 and then install LR CC from the Creative Cloud but there may be an easier way. Any thoughts gratefully accepted.