The smallest positive number divisible by $24, 36$,and $48$ is $\ldots \ldots \ldots \ldots .$

$L.C.M.(115, 25) = \ldots$

Find the $\text{l.c.m.}$ and $\text{g.c.d.}$ of the following by using the fundamental theorem of arithmetic: $84$,$90$,and $120$.

Prove that the following number is irrational: $2+\sqrt{3}$.

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 $a, b \in N$)

$\frac{p}{q}$ is a rational number and for non-negative integers $m$ and $n$,$q = 2^{m} 5^{n}$ if and only if the decimal form of $\frac{p}{q}$ is $\ldots \ldots \ldots \ldots$