Question

The product of three consecutive positive integers is divisible by $6$. Is this statement true or false? Justify your answer.

Answer 1

Let the integer be $=x,x+1,x+2$ .

Given condition: $x(x+1)(x+2)=6$
$x(x+1)(x+2)=1\times 2\times 3$

Compare $x=1,x+1=2$ and $x+2=3$
So the numbers are $1,2,3$

Hence, the given statement is true.