How to Find LCM of Polynomials?
Below are the steps to find the LCM of polynomials.
- First do factorization of the polynomials (using prime factorization).
- Then, find the product of all factors or variables.
- The resultant common term gives the LCM of the given polynomials.
Example: Given three polynomials x2 – y2 and (x + y)2. Find the HCF of these polynomials.
Solution:
First, we do factorization of the given polynomials.
x2 – y2 = (x + y) (x – y)
(x + y)2 = (x + y) (x + y)
Product of all factors = (x + y)3(x – y)
HCF of the given polynomials = (x + y)3(x – y)
HCF and LCM of Polynomials
HCF (Highest Common Factor) and LCM (Least Common Multiple) of polynomials are concepts similar to those for integers. The HCF of two polynomials is the largest polynomial that divides both polynomials without leaving a remainder, while the LCM is the smallest polynomial that is a multiple of both polynomials.
To find the HCF of polynomials, we take the common factors among all the factors of two polynomials, and for LCM, we take the product of all their unique factors. In this article, we will discuss how to find HCF and LCM for polynomials, with some solved examples as well.
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