Question

What is LCM of p^2 and p^2+7p+10

Answer 1

p^4+7p^3+10p^2

Answer 2

that is not correct

Answer 3

Break down both into prime factors so to speak
which is p^2 and (p+2)(p+5)
There is no highest common factor other than 1
Therefore they have to be multiplied to find LCM
Which is
p^2 ( p^2+7p+10) giving p^4+7p^3+10p^2
Think about finding the LCM of 12 and 35
= (3.2^2)and (3.7) the HCF is 1 so we multiply to find LCM
which is 35 x 12 = 420
The same applies to algebra

take a different problem LCM of x^2 +3x +2 and x^2 +6x +5
Factored we get
x^2 +3x +2 = (x+1)(x+2)
x^2 +6x +5 = (x+1)(x+5)

(x+1) is the HCF of both expressions so that is only needed once.
Therefore the LCM is (x+1)(x+2)(x+5)