Open iTunes on your computer. Click on Apps in the list on the left to see all your iOS apps. Click on Check for Updates at the bottom. All of the apps which need updates (including Adobe Reader) should appear. Select which apps (including Reader) that you want to update. Then sync the app to your mobile device.
Alternatively, on your iPhone or iPad, find the App Store app and open it. Click on the Updates button at the bottom. Choose the apps you want to update (including Reader).
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