The common theme that is shared by both speeches is:
B. Freedom for all
The common theme of the two texts is freedom of all. In the first Gettysburg Abraham by Abraham Lincoln, the president encouraged the people to be willing to improve on the sacrifices that their fathers had made earlier on for them.
In the end, he advocated for government by the people and for the people. In this sense, he was promoting freedom for all.
In the second Nobel Prize speech by Martin Luther King, he also encouraged the people to avoid racism so that their children will be proud of their efforts. So, he was promoting freedom for all. So, the two texts share the common theme of freedom for all.
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