Problem on Finding LCM of Numbers (n+2) and (n-3)

Topic : Lowest Common Factor
Question : Find the LCM of (n+2) and (n-3).

Solution :
LCM of (n+2)(n-3)
would be:Case1 : { (n+2)(n-3) for all n/ where (n-3) is not a multiple of 5}
Case2 : { [(n+2)(n-3)/5] for all n/ where (n-3) is a multiple of 5}(this can be solved using the division method of finding the GCF)
n-3)n+2(1
## -n-3
________
#####5--------> remainder
CASE 1 :
let us assume (n-3)=6 (not a multiple of 5)
n =6 +3 = 9
(n+2)(n-3) = 11 x 6= 66 ---> product is the LCM
CASE 2 :
let us assume (n-3)= 5 (multiple of 5)
n = 5+3 = 8
(n+2)(n-3)/5 = 10 x 5/5 = 10---------> is the LCM

I hope this explains how we get the LCM for (n+2)(n-3)