Greatest Common Factor
&
Least Common Multiple
of Monomials
Unit 1, Lesson 3
A1.1.1.2.1
What is a Monomial?
• A monomial is an expression of one
term that consists of a number, a
variable, or the product of a number
and one or more variables.
Example:
Greatest Common Factor
• The greatest common factor
(GCF) is the greatest factor that
evenly divides into a set of numbers
or monomials.
• The greatest common factor is used
when factoring a set of numbers or
monomials.
Finding the GCF
• Find the GCF of the numbers first!
o Find all factors of both numbers.
Select the factors that are common to
both. Choose the greatest.
• Find the GCF of the variables second!
o Select the smallest exponent value for
each variable that appears in each
monomial.
Example
Least Common Multiple
• The least common multiple (LCM)
is the smallest number or expression
that is a common multiple of two or
more numbers or algebraic terms.
Example:
Least Common Multiple
• The LCM is used when adding or
subtracting fractions with unlike
denominators.
oBefore fractions are combined, they
need to be rewritten as equivalent
fractions with like denominators.
oThe LCM becomes the like
denominator of the equivalent
fractions.
Finding the LCM
• Find the LCM of the numbers first!
o Begin listing multiples of each
number. Continue listing multiples until
you get the first match. The first
match among the list of multiples is the
LCM.
• Find the LCM of the variables second!
o Select the largest exponent value for
each variable. Variables DO NOT have
to appear in all monomials!
Example
Practice #1
𝟐 𝟒
𝟒𝟓𝒙 𝒚
Practice #2
𝟐
𝟐𝒙 𝒚
Practice #3
𝟑
𝟕𝒙𝒚
Practice #4
𝟐 𝟑
𝟑
𝟒𝟓𝒖 𝒗 𝒘
Practice #5
𝟒 𝟒 𝟒
𝟏𝟓𝒙 𝒚 𝒛
Practice #6
𝟒
𝟔𝒙𝒚