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Longest common prefix of two strings in bash

I have two strings. For the sake of the example they are set like this:

string1="test toast"
string2="test test"

What I want is to find the overlap starting at the beginning of the strings. With overlap I mean the string "test t" in my above example.

# So I look for the command 
command "$string1" "$string2"
# that outputs:
"test t"

If the strings were string1="atest toast"; string2="test test" they would have no overlap since the check starts from the beginning and the "a" at the start of string1 .

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In sed, assuming the strings don't contain any newline characters:

string1="test toast"
string2="test test"
printf "%s
%s
" "$string1" "$string2" | sed -e 'N;s/^(.*).*
1.*$/1/'

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