1. What are factors and multiples?
LCM & GCF
max 0≤𝑥≤1 𝑥 𝑒 − 𝑥 2 −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎 𝑥+𝑎 𝑛 = 𝑘=0 𝑛 𝑛 𝑘 𝑥 𝑘 𝑎 𝑛−𝑘

2. Multiple A multiple is the product of a given value and something else
What are they?
Factor A factor is a number that can be multiplied by something to get a given value
Multiple A multiple is the product of a given value and something else

3. What Is LcM? LCM stands for least common multiple
The least common multiple is the smallest number that two given numbers are both factors of
Example: the least common multiple of 3 & 6 is 12; 3X4=12 and 6X2=12
**Sometimes the LCM can be found by multiplying the two factors together

4. What is GCF? GCF stands for greatest common factor
The greatest common factor is the largest number that is a factor of one or more given values
Example: the greatest common factor of 12 & 18 is 6 (6X2=12, 6X3=18)
**Sometimes the greatest common factor is one of the given numbers

5. How to find lcm To find LCM:
First, begin listing the multiples of the larger number from least to greatest (remember that the number its self is a multiple)
Check each multiple (in numerical order) to see if the smaller number is a factor
Once you find a number that both numbers are a factor of you have found your answer
**This must be done in numerical order (least to greatest)

6. How to find gcf To find GCF:
First, list all the factors of each number
Order the sets of factors in numerical order (keep the sets separate)
Circle all of the factors that the numbers have in common
The greatest number is the GCF
**Sometimes the GCF is one

7. Lcm & gcf practice
LCM
1:If you are buying plates that come in packages of 4 and napkins that come in packages of 20 how many packages do you need to buy of each so that you will have the same number of each
GCF
2:If you have 14 plates and 21 napkins for a party, what is the greatest number of people that you can invite so that everyone gets the same number of plates and napkins, and none are left over

8. Steps to solve Problem 2: Problem 1:
You need to find the GCF of 14 & 21
The factors of 14 are: 1,2,7,14
The factors of 21 are: 1,3,7,21
The greatest common number is 7
7 is the GCF
Problem 1:
You need to find the LCM of 4 & 20
The first multiple of 20 is 20
Four is a factor of 20
20 is the LCM

9. Answers
Problem 1:
You will need 5 packages of plates and one package of napkins
Problem 2:
You can invite 7 people (everyone will receive 2 plates and 3 napkins)

10. Factor? Multiple? What is a factor? A: the product of two numbers
B: a number that can only be divided equally by its self and one
C: a number that can be multiplied by something to get a given value
What is a multiple?
A: a number that can be divided by more than two different numbers
B: the product of a given value and something else
C: a prime number greater than 2

11. Lcm? GCF? What is LCM? A: Least Common Multiple
B: Largest Common Multiple
C: Least Composite Multiple
What is GCF
A: Greatest Composite Factor
B: Greatest Common Factor
Greatest Common Fraction

12. Multiple choice answers
Factor & Multiple
LCM & GCF
Factor: C (a number that can be multiplied by something else to get a given value
Multiple: B (the product of a given value and something else
LCM: A (least common multiple)
GCF: B (greatest common factor

13. For additional practice