Let us call the largest common divisor of integers $m$ and $n$ by $(m,n)$. For example, $(2,3)=1$ and $(10,15)=5$. Let us assume that $n(n+1)(n+2)$ is a square where $n$ is an integer.
Now I want to find the value of $(n+1,n+2)$ and $(n+1,n(n+2))$ .
To solve this problem I think that the multiplication of two numbers is the multiplication of their LCM and GCD. But I can not proceed after that step.
Can you help me to solve this problem?