Question

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

Answer 1

It is $True$
Let $a=n(n+1)(n+2)$..1
Because out of three consecutive positive integers , one of the integers must be an even integer and one integer as multiple of 3.
let $n=2pandn+1=3q$
$a=2p\left(3q\right)(n+2)=6\left[\left(pq\right)(n+2)\right]=6mwherem=\left[\left(pq\right)(n+2)\right]$