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# LCM of Polynomials

TopThe term LCM refers to Least Common Multiple. For finding the LCM, we need to have two terms. To find the LCM of polynomials, we need to have some knowledge of polynomial. We already know that a polynomial is a mixture of variables and constant. If we are having a function x2 + 3x + 4, then it is a polynomial with degree two.

Degree is the highest power on the variable.

The LCM of two Numbers can be found quite easily. We need to have good knowledge about the factor of the number. We can find out the LCM by choosing the minimum factor.

If we have two number, let say 6 and 22. Then, factor of six will be 3 x 2 and the factors for 22 will be 11 x 2. So, 2 is the least common factor between them. So, the LCM will be 2.

Now, we will take two polynomials and we will find the LCM of those polynomial.

Example:

Find the LCM of the polynomial given below
f(x) = x2 + 5x + 6 and f(x) = x2 + 6x + 8

Solution:

First, we will find the factors of the first polynomial.

The factors of the first polynomial will be

x2 + 3x + 2x + 6
(x2 + 3x) + (2x + 6)
x (x + 3) + 2(x + 3)

Now, we can take x + 3 as common. So, our expression will be,
(x + 2) (x + 3),

Now, we will take the second polynomial.

x2 + 6x + 8,
x2 + 4x +2x + 8,
x (x + 4) + 2(x + 4),

We can take x + 4 as common. So, our expression will be,
(x + 2) (x + 4)

So, in both the expressions, we have (x + 2).
So, the required LCM will be x + 2.