$ \begin{array}{r|l} 6 & 2\\ 3 & 3\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 8 & 2\\ 4 & 2\\ 2 & 2\\ 1 & \end{array} $
6 = 2 * 3;
$8 = 2^3$;
$НОК (6, 8) = 2^3 * 3 = 24$

$ \begin{array}{r|l} 15 & 3\\ 5 & 5\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 25 & 5\\ 5 & 5\\ 1 & \end{array} $
15 = 3 * 5;
$25 = 5^2$;
$НОК (15, 25) = 5^2 * 3 = 75$.

$ \begin{array}{r|l} 16 & 2\\ 8 & 2\\ 4 & 2\\ 2 & 2\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 12 & 2\\ 6 & 2\\ 3 & 3\\ 1 & \end{array} $
$16 = 2^4$;
$12 = 2^2 * 3$;
$НОК (16, 12) = 2^4 * 3 = 48$.

$ \begin{array}{r|l} 48 & 2\\ 24 & 2\\ 12 & 2\\ 6 & 2\\ 3 & 3\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 42 & 2\\ 21 & 3\\ 7 & 7\\ 1 & \end{array} $
$48 = 2^4 * 3$;
42 = 2 * 3 * 7;
$НОК (48, 42) = 2^4 * 3 * 7 = 336$.

$ \begin{array}{r|l} 35 & 5\\ 7 & 7\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 20 & 2\\ 10 & 2\\ 5 & 5\\ 1 & \end{array} $
35 = 5 * 7;
$20 = 2^2 * 5$;
$НОК (35, 20) = 5 * 7 * 2^2 = 140$.

$ \begin{array}{r|l} 56 & 2\\ 28 & 2\\ 14 & 2\\ 7 & 7\\ 1 & \end{array} $
 
$ \begin{array}{r|l} 63 & 3\\ 21 & 3\\ 7 & 7\\ 1 & \end{array} $
$56 = 2^3 * 7$;
$63 = 3^2 * 7$;
$НОК (56, 63) = 3^2 * 7 * 2^3 = 504$.