Question

If $n$ is an even natural number, then which of the following is the largest natural number by which $n(n+1)(n+2)$ is definitely divisible?

• A. $6$
• B. $8$
• C. $12$
• D. $24$

Answer 1

The correct option is D $24$

Out of $n$ and $n+2$, one is divisible by $2$ and the other by $4$, hence $n(n+2)$ is divisible by $8$.
Also $n,n+1,n+2$ are three consecutive numbers, hence one of them is divisible by $3$.
Hence, $n(n+1)(n+2)$ must be divisible by $24$. This will be true for any even number $n$