Question

The product of three consecutive natural numbers is divisible by

• A. $2$
• B. $3$
• C. $4$
• D. $6$

Answer 1

Answer: (A), (B), (D)

$3$
$6$
$2$

Let three consecutive number be, $n+1,n+2,n+3$
Thus their product is, $P=(n+1)(n+2)(n+3)=\frac{n!(n+1)(n+2)(n+3)}{n!}$
$\Rightarrow P=\frac{(n+3)!}{n!3!}\times 3!{=}^{n+3}{C}_3\times 6=6\times$ some Integer
Hence option A,B,D are correct choices