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Created By : Rina Nayak

Reviewed By : Rina Nayak

Last Updated : Apr 17, 2023

All the process of finding the LCM using GCF will be done in spilt seconds. So, enter your input polynomials in boxes of the LCM of Polynomials Using GCF Calculator and make your calculations easier and faster.





LCM of

What is meant by LCM of Polynomials?

The Least common multiple of polynomials or algebraic expression includes the highest number of each of the various factors in the addressed polynomials. The expression of lowest degree or power thus the expressions exactly divide it is called the Least Common Multiple of two or more algebraic (polynomial) equations.

Relation Between H.C.F. and L.C.M. of Two Polynomials

The relation between L.C.M and H.C.F of polynomials is the product of polynomials is equal to the product of its H.C.F and L.C.M. This relationship can be displayed as follows.

p(x) * q(x) = {L.C.M of p(x) and q(x)} * {H.C.F of p(x) and q(x)}.

How to Find Least Common Multiple of Polynomials using GCF Method?

For finding the LCM or Least common multiple of monomials or polynomials with greatest common factor method, you need to follow the simple steps given here:

  1. Initially, determine the factors of all the polynomial equations.
  2. Solve the GCF of the factored polynomial using GCF method.
  3. Later on, multiply the given polynomial expressions to find the LCM.
  4. Now, divide the multiplied polynomial with GCF of polynomial.
  5. Finally, you will obtain the LCM of the polynomial using GCF method.

Solved Example to Get lowest common factor of polynomials using GCD method


Find LCM of x+1, 6y^4-54y^2x^2 Using Greatest Common Factor


Given expressions are x+1, 6y^4-54y^2x^2

First, find the factors for each expression;

The factors of x+1 is x+1

The factors of 6y^4-54y^2x^2 is -6y^2(3x - y)(3x + y)

Now, find the GCF of factored expressions then we get the greatest common factor is 1.

Multiply the given polynomials and move a step forward to find the LCM polynomials using GCF method.

ie.,(x+1)*(6y^4-54y^2x^2) = -54x^3y^2 - 54x^2y^2 + 6xy^4 + 6y^4

Now, you have to divide this resultant by GCf ie., -54x^3y^2 - 54x^2y^2 + 6xy^4 + 6y^4 / 1 = -54x^3y^2 - 54x^2y^2 + 6xy^4 + 6y^4

Hence, the LCM of x+1, 6y^4-54y^2x^2 is -54x^3y^2 - 54x^2y^2 + 6xy^4 + 6y^4.

FAQs on LCM of Polynomials Using GCF Calculator

1. How to find lcm of polynomials?

You can find least common multiple of polynomials by factoring or GCF method or some other approaches.

2. List of LCM of polynomials examples to practice & verify with LCM of Polynomial with GCF Calculator?

Here, we are listing out some of the LCM of polynomials examples that can be solved by using GCF method:

  • LCM of Polynomials (x+6) and 4x^2(x+2)
  • LCM of Polynomials (x^2-8x+7) and (x^2+x-2)
  • LCM of Polynomials (x+3) and (x-3)
  • LCM of Polynomials (x-1) and (x-6)

3. Where can we find the gcd of polynomials calculator with steps?

You can find the greatest common divisor of polynomial calculator with steps from factorpolynomials.com website which is a reliable and trusted one to calculate any of the mathematical concepts.