Perahps not a memory issue, but not enough free disk space.
Click the Apple menu icon top left in your screen. From the drop down menu click About this Mac > More Info > System Report then select Storage on the left under Hardware.
You'll see Available and Capacity. Make sure there's at least 15% free disk space. Not enough disk space can cause apps to quit unexpectedly.
If it's not a disk space issue, try troubleshooting third party plug-ins and extensions.
From your Safari menu bar click Safari > Preferences then select the Security tab.
Deselect: Allow all other plug-ins. Quit and relaunch Safari to test.
If that made a difference, instructions for troubleshooting plugins here.
If it's not a plug-in issue, select the Extensions tab. If there are any extensions installed, turn that OFF, quit and relaunch Safari to test. If that made a difference, uninstall one at a time, quit and relaunch Safari until you find the culprit.