Find the $\text{g.c.d.}$ and $\text{l.c.m.}$ of $8$,$9$,and $25$ using the fundamental theorem of arithmetic.

$A$ bookseller has $56$ English books and $72$ Gujarati books. He wants to stack them in such a way that all the books are stored topic-wise and the height of each stack is the same and also the stacks occupy the least surface area of the bottom. What is the maximum number of books that can be placed in each stack for this purpose?

Simplify: $\frac{1}{\sqrt{6}-\sqrt{5}}-\frac{3}{\sqrt{5}-\sqrt{2}}-\frac{4}{\sqrt{6}+\sqrt{2}}$

If $a$ and $b$ are two odd positive integers such that $a > b,$ then prove that one of the two numbers $\frac{a+b}{2}$ and $\frac{a-b}{2}$ is odd and other is even.

For any positive integer $n,$ prove that $n^{3}-n$ is divisible by $6.$

Which of the following groups correctly matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1. \text{l.c.m.}(8, 16, 24)$	$a. 36$
$2. \text{g.c.d.}(8, 16, 24)$	$b. 48$
$3. \text{l.c.m.}(6, 12, 18)$	$c. 8$
$4. \text{g.c.d.}(6, 12, 18)$	$d. 12$
	$e. 6$