1. Greatest Common Factor & Least Common Multiple

2. We are learning to use prime factorization to identify common factors and common multiples
Learning Goal

3. Greatest Common Factor (GCF)
Greatest whole number that divides into two or more other whole numbers with no remainder
Ex: The GCF of 14 & 35 is 7, since 7 is the greatest number that goes into both 14 & 35 evenly
Greatest Common Factor (GCF)

4. How to Find the GCF using Prime Factorization
Step 1: Find the prime factors of each number using desired method.
Ex. Find the GCF of 225 & 30
How to Find the GCF using Prime Factorization

5. How to Find the GCF using Prime Factorization
Step 2: Arrange the prime factors in a Venn diagram with the common prime factors in the overlap.
Ex.
How to Find the GCF using Prime Factorization 5 3 2
Prime Factors
Of 225
Prime Factors
Of 30 3 5

6. How to Find the GCF using Prime Factorization
Step 3: Multiply the common prime factors to find the GCF (numbers in overlap).
Ex.
GCF of 225 & 30 is 3 x 5
GCF of 225 & 30= 15
How to Find the GCF using Prime Factorization

7. Try It Out Find the GCF of 36 & 48 36 = 2 x 2 x 3 x 3
48 = 2 x 2 x 2 x 2 x 3
GCF is 2 x 2 x 3
GCF = 12
Try It Out

8. The least whole number that has two or more given numbers as factors (the lowest number that is a multiple of each of the numbers).
Ex. The LCM of 12 & 9 is 36 since both 12 & 9 divide evenly into 36.
Hint: Think of Common Denominators in Fractions.
Least Common Multiple
A common denominator is the LCM of the denominators.

9. How to Find the LCM using Prime Factorization
Step 1: Find the prime factors of each number using desired method.
Ex. Find the LCM of 225 & 30
How to Find the LCM using Prime Factorization

10. How to Find the LCM using Prime Factorization
Step 2: Arrange the prime factors in a Venn diagram with the common prime factors in the overlap.
Ex.
How to Find the LCM using Prime Factorization 5 3 2
Prime Factors
Of 225
Prime Factors
Of 30 3 5

11. How to Find the LCM using Prime Factorization
Step 3: Multiply all prime factors in the circles (common prime factors by all other factors)
Ex.
LCM of 225 & 30 is 5 x 3 x 3 x5 x 2
LCM of 225 & 30 = 450
How to Find the LCM using Prime Factorization

12. Try It Out Find the LCM of 36 & 48 36 = 2 x 2 x 3 x 3
48 = 2 x 2 x 2 x 2 x 3
LCM is 2 x 2 x 3 x 2 x 3 x 2
LCM = 144
Try It Out

13. GCF & LCM Problem-Solving
How can you tell if a word problem requires you to use Greatest Common Factor or Least Common Multiple to solve?
GCF & LCM Problem-Solving

14. Is it a GCF Problem? What is the question asking us?
Do we have to split things into smaller sections?
Are we trying to figure out how many people we can invite?
Are we trying to arrange something into rows or groups?
Is it a GCF Problem?

15. Is it an LCM Problem? What is the question asking us?
Do we have an event that is or will be repeating over and over?
Will we have to purchase or get multiple items in order to have enough?
Are we trying to figure out when something will happen again at the same time?
Is it an LCM Problem?