I also stucked in the same problem. Below solution works for me.
It would be better if you upgrade your node and npm versions to latest. After that please follow the below steps to install the angular/cli:
Open your command prompt with administrative privileges and uninstall angular/cli by using npm uninstall -g angular-cli command.
Remove node_modules directory and then clear the cache by using npm cache clear --force command.
Remove C:\Users\<username>\AppData\Roaming\npm\ and C:\Users\<username>\AppData\Roaming\npm-cache.
Try to install the angular/cli@latest by using npm install -g @angular/cli@latest command.
Hope the above trick resolve your issue.