Enter the values of GCF, LCM to find the Common Monomial Factor with our basic and advanced calculator.
Common Monomial Factor Calculator
The Common Monomial Factor (CMF) calculator is used in algebra to find the common monomial factor of two or more algebraic expressions. It represents the term that can be factored out from each expression, simplifying the expressions and aiding in further algebraic operations.
Formula:
The formula is:
$\text{CMF} = \text{GCF} \times \text{LCM}$
Variables
Variable  Meaning 

CMF  Common Monomial Factor (the product of the Greatest Common Factor and the Least Common Multiple) 
GCF  Greatest Common Factor (the largest factor common to the given monomials) 
LCM  Least Common Multiple (the smallest multiple common to the given monomials) 
How to Calculate:

Determine GCF and LCM: Find the greatest common factor (GCF) and least common multiple (LCM) of the given expressions.

Apply Formula: Multiply the GCF by the LCM to obtain the common monomial factor (CMF).
Solved Examples:
Example 1:
Given:
 Monomials: $12x^2y$ and $18xy^2$
Calculation  Instructions 

Step 1: GCF = $6xy$  Find the GCF of $12x^2y$ and $18xy^2$ which is $6xy$ 
Step 2: LCM = $36x^2y^2$  Find the LCM of $12x^2y$and $18xy^2$, which is $36x^2y^2$. 
Step 3: CMF = $6xy \times 36x^2y^2$  Multiply the GCF by the LCM. 
Step 4: CMF = $216x^3y^3$  Simplify the expression to find the Common Monomial Factor. 
Answer:
The Common Monomial Factor is $216x^3y^3$.
Example 2:
Given:
 Monomials: $8a^3b$ and $12ab^2$
Calculation  Instructions 

Step 1: GCF = $4ab$  Find the GCF of $8a^3b$ and $12ab^2$ which is $4ab$. 
Step 2: LCM = $24a^3b^2$  Find the LCM of $8a^3b$ and $12ab^2$, which is $24a^3b^2$. 
Step 3: CMF = $4ab \times 24a^3b^2$  Multiply the GCF by the LCM. 
Step 4: CMF = $96a^4b^3$  Simplify the expression to find the Common Monomial Factor. 
Answer:
The Common Monomial Factor is $96a^4b^3$.
What is the Common Monomial Factor Calculator?
The Common Monomial Factor Calculator helps you to find the product of the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of given monomials. It represents the highest expression that can divide all the given monomials without leaving a remainder.
The formula helps in simplifying algebraic expressions, solving polynomial equations, and factoring monomials in algebra. It is important in algebra, where it helps students and mathematicians to simplify and solve complex algebraic problems by breaking them down into their most basic factors and multiples.
Conclusion:
In the field of algebra, the Common Monomial Factor calculator is very important. Because it provides a systematic way to simplify different algebraic equations to find out the common monomial factor among them.