Question

If $n$ is a natural number then $n(n+1)(n+2)$ is always divisible by

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$

Given that $n$ is a natural number

If $n$ is even then $n,n+2$ are divisible by $2$

If $n$ is odd , then $n+1$ is divisible by $2$

Therefore $n(n+1)(n+2)$ is always divisible by $2$

If we take three consecutive numbers , then there should be a multiple of $3$ among them

Therefore $n(n+1)(n+2)$ is divisible by $3$

Therefore $n(n+1)(n+2)$ is divisible by $2\times 3=6$

So the correct option is $C$