This document discusses finding the greatest common factor (GCF) and least common multiple (LCM) of numbers. It defines GCF as the highest number that divides all given numbers and LCM as the least number that is a multiple of all given numbers. Examples are provided of finding GCF and LCM using listing factors/multiples and continuous division methods. Properties of GCF and LCM are outlined. Practice problems are given to find the GCF of number sets using any method.

1. LESSON 5
Greatest common
factor and Least
common Multiple

2. GOAL/OBJECTIVE
Identifying and Solving
problems involving
Greatest Common
Factor and Least
Common Multiple

3. REVIEW
Write all possible factors of the
following numbers
1. 8 : 1, 2, 4 ,8
2. 10 : 1, 2, 5, 10
3. 7 : 1, 7
4. 12 : 1, 2, 3, 4, 6, 12
5. 30: 1, 2, 3, 5, 6, 10, 15, 30

4. REVIEW
Write the first 5 multiples of the following
numbers
1. 6 : 6, 12, 18, 24, 30
2. 4: 4, 8, 12, 16, 20
3. 15: 15, 30, 45, 60, 75
4. 12: 12, 24, 36, 48, 60
5. 20 : 20, 40, 60, 80, 100

5. DEFINITION OF TERMS
GREATEST COMMON FACTOR
(GCF) - Highest number that
divides exactly all given numbers
LEAST COMMON MULTIPLE
(LCM)- Least natural number that
is a multiple of all given numbers

6. EXAMPLES
Find the GCF of the following numbers using the
Listing method and continuous division
1. 8 and 20
Listing Method
8 : 1, 2, 4, 8
20 : 1, 2, 4, 5, 10, 20
Common Factors: 1, 2, 4
Greatest Common Factor = 4

7. Continuous Division Method
2 8 20
2 4 10
2 5
Greatest Common Factor = 2 x 2 = 4

8. 2. 32, 64, and 56
Listing Method
32: 1, 2, 4, 8, 16, 32
64: 1,2 ,4, 8, 16, 32, 64
56: 1, 2, 4, 7, 8, 14, 28, 56
Common Factors: 1,2,4,8
Greatest Common Factor = 8

9. Continuous Division Method
2 32 64 56
2 16 32 28
2 8 16 14
4 8 7
Greatest Common Factor = 2 x 2 x 2 = 8

10. LEAST COMMON MULTIPLE
Find the LCM of the following numbers using Listing
Method and Continuous Division
1. 4 and 6
Listing Method
4: 4, 8, 12, 16, 20, 24, 28, 30 …
6: 6, 12, 18, 24, 30, 36, …
Common Multiples : 12, 24, 30
Least Common Multiple = 12

11. Continuous Division Method
2 4 6
2 3
Least Common Multiple = 2 x 2 x 3 = 12

12. 2. 10, 24 and 12
Listing Method
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110,120, …
24: 24, 48, 72, 96, 120,…
12: 12, 24, 36, 48, 60, 72, 84, 96, 102, 120,…
Least Common Multiple = 120

13. Continuous Division Method
2 10 24 12
2 5 12 6
3 5 6 3
5 2 1
Least Common Multiple = 2 x 2 x 3 x 5 x 2 x 1= 120

14. PROBLEM SOLVING
1. The principal of a school wishes to distribute 84
balls and 108 bats equally among a number of
boys. Find the greatest number of boys who will
receive the gift in this way.
Solution:
2 84 108
2 42 54
3 21 27
7 9
Answer: 2 x 2 x 3 = 12 boys

15. 2. Four bells ring simultaneously and afterwards at
intervals of 3, 4, 5 and 6 seconds, respectively. At
what interval will they all ring together?
Solution:
2 3 4 5 6
3 3 2 5 3
1 2 5 1
Answer : 2 x 3 x 1 x 2 x 5 x 1 = 60 seconds

16. PROPERTIES OF GCF AND LCM
The GCF of given numbers is not
greater than any of the given
numbers
The GCF of two relatively primes
is 1
The LCM of given numbers is not
less than any of the given
numbers
The LCM of two relatively primes
is equal to their product

17. PRACTICE
Find the GCF of the following numbers
using any method. Write your solution
and final answer on your notebook.
GCF LCM
1. 24 and 16 4. 4, 2 and 3
2. 100, 70 and 50 5. 10, 2 and 5
3. 84, 120, and 156 6. 2, 9 and 8

18. CHECKING

19. PRACTICE
Find the GCF of the following numbers using
any method. Write your solution and final
answer on your notebook.
GCF LCM
1. 24 and 16 = 8 4. 4, 2 and 3 = 12
2. 100, 70 and 50 = 10 5. 10, 2 and 5 = 10
3. 84, 120, and 156 = 12 6. 2, 9 and 8 = 72