This document discusses factors, multiples, least common multiples (LCM), and greatest common factors (GCF). It provides examples of finding the multiples of numbers by multiplying them by counting numbers. It also shows how to find the LCM and GCF of two numbers by listing their common multiples or factors and taking the least or greatest. The key steps are to find the multiples of each number, identify their common multiples to determine the LCM, or common factors to determine the GCF.

1. MATH
Factors and Multiples

2. Drill

3. 5
x7
35

4. 8
x8
64

5. 7
x 9
63

6. 4
x8
32

7. 78
x 0
0

8. 15
x 1
15

9. Factors and Multiples

10. Let us multiply 1, 2, 3,4, 5, 6, 7, 8, 9, 10, 11, and 12 by 2.

11. We can get the multiples of 2 when we count by 2s.
The numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24 are the
multiples of 2.

12. These are MULTIPLES OF 3.
If we multiple the numbers 1 to 12 by 3, we get the numbers:
3 6 9 12 15 18 21 24 27 30 33 36
We generate the multiples of 3 when we count by 3s.

13. NOTE:
When we multiply the set of counting numbers by 4, we get the
multiples of 4.
When we multiply the set of counting numbers by 5, we get the
multiples of 5.
When we multiply the set of counting numbers by 6, we get the
multiples of 6 and so on.

14. LEAST COMMON MULTIPLE
(LCM)

15. Let us get the multiples of 2 and 3 and their common multiples.
The least of all the common multiples is 6.
MULTIPLES OF 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 …
MULTIPLES OF 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 …
COMMON MULTIPLES OF 2 AND 3: 6, 12, 18, 24…
Hence, 6 is called the least common multiple
or LCM of 2 and 3.

16. Try this! Get the LCM of 3 and 4.
MULTIPLES OF 3:
MULTIPLES OF 4:
COMMON
MULTIPLES OF 3
AND 4:

17. Get the LCM of 6 and 9.
MULTIPLES OF 6:
MULTIPLES OF 9:
COMMON
MULTIPLES OF 6
AND 9:

18. GREATEST COMMON FACTOR
(GCF)

19. The pupils of Mr. Razon gave the following answers.
1 x 36 = 36 4 x 9 = 36 18 x 2 = 36 6 x 6 = 36 12 x 3 = 36
The numbers 1, 2, 3, 4, 6, 9, 12, 18, and 36 are the factors of 36.

20. Another example:
3 and 8 1 and 24 6 and 4 12 and 2
The numbers 1, 2, 3, 4, 6, 8, 12, and and 24 are the factors of 24.
Give all the pairs of factors of 24.

21. Let us list down the factors of 24 and 36 and their common factors.
Note that 12 is the greatest of all the common factors of 24 and 36.
Factors of 24:
Factors of 36:
COMMON FACTORS
OF 24 AND 36:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 12
Hence, 12 is the greatest common factor of 24 and 36.

22. We can use the PRIME FACTORIZATION METHOD.
36
2 18
x
9
2 x
3 3
x
24
2 12
2
x
x 6
2 x 3
24: 2 x 2 x 2 x 3
36: 2 x 2 x 3 x 3
2 2
x x 3 = 12 GCF = 12
Factor Tree

23. REMEMBER:
a. The numbers that we multiply are called factors.
b. The multiples of a number are the products of the number and the
set of counting numbers.
c. When the common multiples of two numbers are listed in
increasing order, the first number is the LCM.
d. When the factors of two numbers are listed in increasing order,
the last number is the GCF.

24. Let’s have some
exercises!

27. End