$ \begin{array}{r|l} 19 & 19\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 10 & 2\\ 5 & 5\\ 1 & \end{array} $
19 = 1 * 19;
10 = 1 * 2 * 5;
НОК (19, 10) = 2 * 5 * 19 = 190.

110 = 11 * 10;
НОК (11, 110) = 110.

52 = 26 * 2;
НОК (26, 52) = 52.

НОК (11, 23) = 11 * 23 = 253

$ \begin{array}{r|l} 88 & 2\\ 44 & 2\\ 22 & 2\\ 11 & 11\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 66 & 2\\ 33 & 3\\ 11 & 11\\ 1 & \end{array} $
$88 = 2^3 * 11$;
66 = 2 * 3 * 11.
$НОК (88, 66) = 2^3 * 11 * 3 = 264.$

198 = 9 * 22;
НОК (198, 9) = 198.