4.2 Models for Greatest Common
Factor and Least Common Multiple
•
Vocabulary
o Greatest Common Factor
§ Abbreviated: GCF(a, b)
§ Also called the Greatest Common Divisor or GCD(a,
b)
§ GCF can be found for two or more numbers
§ GCF is the largest number that is a factor of ALL
the numbers being tested
§ Factorization or prime factorization of the
numbers being tested is one way of determining
the largest common factor
• Factors of 12: 1, 2, 3, 4, 6, 12
• Factors of 18: 1, 2, 3, 6, 9, 18
• Then the GCF(12, 18) = 6
§ Alternate method useful when numbers are larger
or when have 3 or more numbers
•
•
The GCF(60, 90) is found by multiplying
together all of the numbers in the vertical
column to the left: 2 x 3 x 5 = 30
•
•
o
This method does not require division by
primes
Least Common Multiple
§ Abbreviated: LCM(a, b)
§ LCM can be found for two or more numbers
§ LCM is the smallest number that is a multiple of
ALL the numbers being tested
§ Listing multiples of the numbers being tested is
one way of determining the smallest common
multiple
• Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96,
108, ...
• Multiples of 18: 18, 36, 54, 72, 90, 108, ...
• Then the LCM(12, 18) = 36
§ Alternate method useful when numbers are larger
or when have 3 or more numbers
•
•
•
The LCM(60, 90) is found by multiplying
together all of the numbers in the "L" shape: 2
x 3 x 5 x 2 x 3 = 180
Checking your answers
Multiply together the original numbers, (a, b), you are
testing: 12 x 18 = 216
o Multiply together the GCF(12, 18) and the LCM(12, 18):
6 x 36 = 216
o The products should be EQUAL: 216 = 216
o IF the GCF(60, 90) = 30 and the LCM(60, 90) = 180,
then GCF(60, 90) x LCM(60, 90) = 60 x 90.
We will do #1 and #2b in class together
In your group do #2
o Practice using an alternate method for each problem
We will do #7 in class together
In your group do #8
o Practice using an alternate method for each problem
Do #3 through #6 and #9 as homework
o Practice using an alternate method for each problem
o
•
•
•
•
•