Find the smallest five-digit number which is exactly divisible by $15$,$55$,and $99$.

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{15}{1600}$

Find the $\text{l.c.m.}$ and $\text{g.c.d.}$ of the following by using the fundamental theorem of arithmetic: $96$ and $404$.

The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $0.02003000400005 \ldots$

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

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

The product of the greatest common divisor ($G$.$C$.$D$.) and the least common multiple ($L$.$C$.$M$.) of two positive integers $a$ and $b$ is equal to: (where $a, b \in N$)