The $HCF$ of $25$ and $52$ is $1$.

Find the smallest integer that is divisible by both $28$ and $63$.

The Least Common Multiple $(LCM)$ of the smallest prime number and the smallest composite number is . . . . . . .

Prove that the number $\sqrt{2}$ is irrational.

If the $HCF(a, b) = 16$, then which of the following cannot be the $LCM(a, b)$? (Options: $32, 72, 64$)

Find the remainder when $p(x) = 40x^2 + 11x - 63$ is divided by $x + 2$.