1. Finding GCF’s and LCM’s
Grade 6

2. Study Island Responders
Do Now (Pre-Test)
Study Island Responders
5 minutes

3. Learning Objective Students will be able to identify factors
and multiples of a positive integer,
common factors, common multiples,
the greatest common factor, and the
least common multiple of a set of
positive integers. 5N13 - Calculate multiples
of a whole number and the least common multiple
of two numbers 5N14 - Identify the factors of a
given number 5N15 - Find the common factors and
the greatest common factor of two numbers

4. Vocabulary
GCF – the factor with the greatest value that is shared by all numbers.
Multiples – the product of a number and a non zero number.
LCM – the multiple with the least value that is shared by all numbers.

5. Finding the Greatest Common Factor
of Two Numbers
We are looking for a factor. The factor
must be common to both numbers. We
need to pick the greatest of such
common factors.

6. The GCF of 36 and 90
Method 1
1) List the factors of each number.
36:
90:
2) Circle the common factors.
3) The greatest of these will be your Greatest Common Factor: 18

7. The GCF of 36 and 90
Method 2
1) Prime factor each number.
36 = 2 ● 2 ● 3 ● 3
90 = 2 ● 3 ● 3 ● 5
2) Circle each pair of common prime factors.
3) The product of these common prime factors will be
2 ● 3 ● 3 = 18
the Greatest Common Factor:

8. Finding the Least Common Multiple
of Two Numbers
We are looking for a multiple. The multiple
must be common to both numbers. We
need to pick the least of such
common multiples.

9. The LCM of 12 and 15
Method 1
1) List the first few multiples of each number.
12:
15:
2) Circle the common multiples.
3) The least of these will be your Least Common Multiple: 60

10. 12 = 2 ● 2 ● 3 15 = 5 ● 3 3 ● 2 ● 2 ● 5 = 60 The LCM of 12 and 15.
Method 2
1) Prime factor each number.
12 = 2 ● 2 ● 3
15 = 5 ● 3
2) Circle each pair of common prime factors.
3) Circle each remaining prime factor.
4) Multiply together one factor from each circle to get the
3 ● 2 ● 2 ● 5 = 60
Least Common Multiple :
Note that the common factor, 3, was only used once.

11. Method 3: Find both GCF and LCM at Once.
The GCF and LCM of 72 and 90
1) Make the following table. 72 90 9 2 8 10 4 5
2) Divide each number by a common factor.
3) Divide the new numbers by a common factor.
Repeat this process until there is no longer a common factor.
The product of the factors on the left is the GCF:
The product of the factors on the left AND bottom is the LCM:
9 ● 2 = 18
9 ● 2 ● 4 ● 5 = 360

12. Method 3: Find both GCF and LCM at Once.
One more example: The GCF and LCM of 96 and 144
1) Make the following table.
Note that you can pick any common factor to start and any remaining common factor for each step. Try starting by dividing by 3 to see that this is so. 96
144 2 6 48 72 4 8 12 2 3
2) Divide each number by a common factor.
3) Divide the new numbers by a common factor.
4) Repeat this process until there is no longer a common factor.
The product of the factors on the left is the GCF:
The product of the factors on the left AND bottom is the LCM:
2 ● 6 ● 4 = 48
2 ● 6 ● 4 ● 2 ● 3 = 288

13. Independent Practice
Group 1
Group 2
Group 3

14. Quick Quiz Study Island (Responders) “Games”

15. Journal & Summary
Nine people plan to share equally 24 stamps from one set and 36 stamps from another set. Explain why 9 people cannot share the stamps equally.
What's is the LCM for two numbers that have no common factors greater than 1? Explain your reasoning.
Nine is not a common factor of 24 and 36. The LCM will be the product of the two numbers.