Live streaming? You mean an internet "radio" station?
There are a number of services out there that will do that for you. You sign up with one, install their app on your own computer to do the broadcasts and embed their player on your website. I haven't reviewed any of these so can't vouch for any one in particular but Google will find you a selection. I don't know about costs, they will vary depending on how much broadcasting time you want to book. One I looked at ranges from USD100 per year for 3 hours a day up to USD500 for 24*7