At my work I am using Xcode 4.5 (Don't ask me why). The iPhone and iPads I am using for testing runs iOS 7. When I plug in the device to run the app on the device it is not being recognized by Xcode since the latest version of SDK on Xcode 4.5 is iOS 6. In other words there is no way to install the app targeted to iOS 6 on a device running iOS 7 using Xcode 4.5.
But there is!!
Plug your device into a laptop that has Xcode 5. It will recognize the device and show the name of the device in the Xcode device selector. Once, all the device information has been downloaded you can unplug the device and connect it to the Mac running Xcode 4.5. Now that computer will also recognize the device and you can install your iOS 6 app on the device running iOS 7.
Please note that although you can install the app you will not be able to debug the app!!