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

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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**.

There are 2 expressions:

c^2+4c+3 and c+3.

The least common multiple is an expression which is least possible mulple(LCM) of both c+3 and c^2+4x+3.

Since first expression is of higher degree we would like to see whether it has any factor, whether there is a highest common factor between the two expressions.

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

So c+3 is therefore the HCF(hoghest common factor).

Therefore the LCM of the two expressions or numbers = product of the given two expresions or numbers/HCF of these two given expressions or numbers)

= (c^2+4c+3)(c+3)/(c+3) = c^2+4c+3 is, therefore, the LCM of c^2+4c+3 and c+3.

To find the least common multiples of the two given expression we first factorize the first expression in the following steps>

c^2 + 4c + 3

c^2 + c + 3c + 3

c(c + 1) + 3(c + 1)

(c + 1)(c + 3)

From above factors we see that one of the factors of the first expression is (c + 3), which is same as the second given expression.

Thus first expression is a multiple of second expression. Also the first expression is the least multiple of it self. Thus the first expression is the least common multiple of both the expression.

Answer:

Least common multiple is: c^2 + 4c + 3