how do i connect my iPad air to my LG smart TV

You can purchase an apple TV and use to connect your iPad via Airplay. Alternatively, you can purchase this adapter (+ HDMI cable):

Lightning Digital AV Adapter - Apple Store (U.S.)

Third party software may exist, google around. There is no way to natively do this, however.

You can connect via a cable or wireless using an Apple TV.

http://ipad.about.com/od/iPad_Guide/a/How-To-Connect-Your-Ipad-To-Your-Tv.htmhttp://ipad.about.com/od/iPad_Guide/a/How-To-Connect-Your-Ipad-To-Your-Tv.htm

Connect an iPad to a Television or Projector

http://www.everymac.com/systems/apple/ipad/ipad-faq/how-to-connect-ipad-to-tv-te levision-projector.htmlhttp://www.everymac.com/systems/apple/ipad/ipad-faq/how-to-connect-ipad-to-tv-te levision-projector.html

Connecting iPad iPhone or iPod to TV or Projector

http://www.disabled-world.com/assistivedevices/computer/ipad-tv.phphttp://www.disabled-world.com/assistivedevices/computer/ipad-tv.php

iPad Accessories: Connections for a TV or Projector

http://www.dummies.com/how-to/content/ipad-accessories-connections-for-a-tv-or-p rojector.htmlhttp://www.dummies.com/how-to/content/ipad-accessories-connections-for-a-tv-or-p rojector.html

You may be interested in AirPlay on the Apple TV:

http://www.apple.com/airplay/http://www.apple.com/airplay/

http://www.apple.com/airplay/http://www.apple.com/airplay/

Alternately, there are Apple Digital AV Adapters for hardwired connections:

http://support.apple.com/kb/ht4108http://support.apple.com/kb/ht4108

http://support.apple.com/kb/ht4108http://support.apple.com/kb/ht4108

You may need a LG app.

 Cheers, Tom 😉

You're welcome. Best of luck.