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As you know the default PHP version for Ubuntu 16.04 is 7.0. If you want to install a new version of PHP on 16.04 you need to use an additional PPA (as it is shown below) or you must compile it on your own.

# Add the repository 'ppa:ondrej/php'

sudo apt-get install software-properties-common
sudo add-apt-repository ppa:ondrej/php
sudo apt update

# Install PHP 7.2

sudo apt install -y php7.2 php7.2-cli libapache2-mod-php7.2
sudo apt install -y php-imagick php-gettext php-memcache php-apcu php-pear php-xml php-xmlrpc
sudo apt install -y php-memcached php-mysql php-intl php-mbstring php-curl php-gd php-imagick
sudo apt install -y php7.2-common php7.2-mysql php7.2-cgi 
sudo apt install -y php7.2-curl php7.2-zip php7.2-mbstring php7.2-xmlrpc php7.2-gd php7.2-xml php7.2-xsl
sudo apt install -y php7.2-dev php7.2-bz2 php7.2-intl php7.2-json php7.2-opcache php7.2-readline 
sudo apt install -y php7.2-imap php7.2-pspell php7.2-recode php7.2-sqlite3 php7.2-tidy php7.2-bcmath #php7.2-mcrypt

# Update the Apache's PHP version

sudo a2dismod php7.0
sudo a2enmod php7.2
sudo systemctl restart apache2.service

# Update the CLI PHP version

sudo update-alternatives --set php /usr/bin/php7.2

Now you can see PHP version

php -v
PHP 7.2.33-1+ubuntu16.04.1+deb.sury.org+1 (cli) (built: Aug  7 2020 14:43:59) ( NTS )
Copyright (c) 1997-2018 The PHP Group
Zend Engine v3.2.0, Copyright (c) 1998-2018 Zend Technologies
    with Zend OPcache v7.2.33-1+ubuntu16.04.1+deb.sury.org+1, Copyright (c) 1999-2018, by Zend Technologies