What is the Least Common Multiple?c^2+4c+3 and c+3 What is the Least Common Multiple of these two numbers?

Knowing the fact that LCM of 2 or more numbers, is the
smallest number which could e found, so that this one to be divided by each number from
the given set of numbers, we have to factor each of the given numbers, into it's prime
factors.

Let's factor
c+3=1*(c+3).

Now, let's factor c^2+4c+3. Noticing that the
expression c^2+4c+3 is a second degree polynomial, we'll write it's equation and find
it's roots in order to write the polynomial as a product of linear
factors.

 c^2+4c+3=0

c1 =
[-4+sqrt(16-12)]/2

c1 =
(-4+2)/2

c1 = -1

c2 =
(-4-2)/2

c2 = -3

So, the
polynomial  c^2+4c+3, could be writtenas:

 c^2+4c+3 =
(c-(-1))(c-(-3)) = (c+1)(c+3)

So, the prime factors
of  c^2+4c+3 are (c+1) and (c+3).

It is obvious that the
number c^2+4c+3 could be divided by (c+3) and the number (c+3) could be divided by
itself.

So, the LCM of the
numbers c^2+4c+3 and c+3 is c+3.