Basic Mathematics for College Students

What is the greatest number of times

a. 2 appears in any one factorization?

b. 3 appears in any one factorization?

c. 5 appears in any one factorization?

d. Fill in the blanks to find the LCM of 36 and 90:

10. The prime factorizations of and 140 are:

What is the greatest number of times

a. 2 appears in any one factorization?

b. 5 appears in any one factorization?

c. 7 appears in any one factorization?

d. Fill in the blanks to find the LCM of

and 140:

11. The prime factorizations of 12 and 54 are:

What is the greatest number of times

a. 2 appears in any one factorization?

b. 3 appears in any one factorization?

c. Fill in the blanks to find the LCM of 12 and 54:

12. The factors of 18 and 45 are shown below.

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 45: 1, 3, 5, 9, 15, 45

a. Circle the common factors of 18 and 45.

b. What is the GCF of 18 and 45?

13. The prime factorizations of 60 and 90 are:

a. Circle the common prime factors of

60 and 90.

b. What is the GCF of 60 and 90?

14. The prime factorizations of and 132 are:

a. Circle the common factors of and 132.

b. What is the GCF of 36, 84,and 132?

36, 84,

132  2  2  3  11

84  2  2  3  7

36  2  2  3  3

36, 84,

90  2  3  3  5

60  2  2  3  5

LCM 2  3 

54  21  33

12  22  31

LCM    

14, 70,

140  2  2  5  7

70  2  5  7

14  2  7

14, 70,

LCM     

15. a. The abbreviation for the greatest common factor
    is.
    b. The abbreviation for the least common multiple is
    .


16. a. We read LCM as “The
    multiple 2 and 15 30.”
    b. We read GCF as “The
    factor 18 and 24 6.”

Find the first eight multiples of each number.See Example 1.

17. 4 18. 2

19. 11 20. 10

21. 8 22. 9

23. 20 24. 30

Find the LCM of the given numbers.See Example 2.

25. 
    
    
    
    26. 
        
    
    
    
    


26. 
    
    
    
    28. 
        
    
    
    
    


27. 
    
    
    
    30. 
        
    
    
    
    


28. 
    
    
    
    32. 
        
    
    
    
    

Find the LCM of the given numbers.See Example 3.

33. 
    
    
    
    34. 
        
    
    
    
    


34. 
    
    
    
    36. 
        
    
    
    
    

Find the LCM of the given numbers.See Example 4.

37. 
    
    
    
    38. 
        
    
    
    
    


38. 
    
    
    
    40. 
        
    
    
    
    


39. 
    
    
    
    42. 
        
    
    
    
    


40. 
    
    
    
    44. 
        
    
    
    
    

Find the LCM of the given numbers.See Example 5.

45. 
    
    
    
    46. 
        
    
    
    
    


46. 
    
    
    
    48. 
        
    
    
    
    

Find the GCF of the given numbers.See Example 7.

49. 
    
    
    
    50. 
        
    
    
    
    


50. 9, 12 52.10, 12

4, 6 6, 15

5, 12, 15 8, 12, 16

6, 24, 36 6, 10, 18

100, 120 120, 180

35, 45 36, 48

30, 50 21, 27

16, 20 14, 21

2, 3, 10 3, 6, 15

3, 4, 6 2, 3, 8

4, 7 5, 8

5, 11 7, 11

8, 12 10, 25

3, 5 6, 9

GUIDED PRACTICE

(18, 24) 6

(2, 15) 30

NOTATION

1.8 The Least Common Multiple and the Greatest Common Factor 99