Question

Which two consecutiv enen numbers have an LCM of $180$?

Answer 1

We have,

Let $2n$ and $2(n+1)$ be the consecutive numbers.Then,

$2n=2\times n$

$2(n+1)=2\times n\times (n+1)$

Therefore,

$\begin{array}{c}2n\left(n+1\right)=180\\ n\left(n+1\right)=90\\ n^2+n-90=0\\ \left(n+10\right)\left(n-9\right)=0\\ n=9,n>0\\ 2n=18\\ 2\left(n+1\right)=20\end{array}$

Numbers are $18$ and $20$