How to Find HCF and LCM of Polynomials
Prime factorization is the most common method to determine the HCF and LCM of algebraic expressions. The following are the steps to take in order to determine the HCF and LCM of an algebraic expression are given below.
- Firstly, Write down the given algebraic expressions.
- Then, determine which terms belong in each algebraic expression.
- After that, Find the prime factors of each term.
- At last, Take the common of all the prime factors of two polynomials to get the HCF of an algebraic expression and take the product of all of the algebraic expression’s prime components to find the LCM.
Example: Find the HCF and LCM of the algebraic expressions 6x3y2, 10x4y4 and 30x4y3.
Solution:
- 6x3 y2 = 6 × x3 × y2
- 10x4y4 = 10 × x4 × y4
- 30x4y3 = 30 × x4 × y3
HCF = 2 × x3 × y2 = 2x3 y2
LCM = 30x4 y4
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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