$LCM(40, 60, 80) = \dots$

Prove that one and only one out of $n, n+2$ and $n+4$ is divisible by $3,$ where $n$ is any positive integer.

If two positive integers $p$ and $q$ can be expressed as $p = a b^{2}$ and $q = a^{3} b$,where $a$ and $b$ are prime numbers,then $LCM(p, q)$ is:

Show that the square of any positive integer cannot be of the form $6m+2$ or $6m+5$ for any integer $m$.

Why are the following numbers composite? Explain: $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$

Find the square root of the expression $56-24 \sqrt{5}$ in the form of a binomial surd.