MATL, 4 bytes
BSXB
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Explanation
% Implicitly grab input as an array
% STACK: [10, 17, 19, 23]
B % Convert each element to binary where each decimal number results in a row
% STACK: [0 1 0 1 0;
% 1 0 0 0 1;
% 1 0 0 1 1;
% 1 0 1 1 1]
S % Sort each column, placing all of the 1's at the bottom of each column
% STACK: [0 0 0 0 0;
% 1 0 0 1 1;
% 1 0 0 1 1;
% 1 1 1 1 1]
XB % Convert each row from its binary representation to its decimal number
% STACK: [0, 19, 19, 31]
% Implicitly display the result