Basic Mathematics for College Students

Chapter 1 Summary and Review 125

Find the LCM of 3 and 5.

Multiples of 5:...

Not divisible Not divisible Divisible by 3.

by 3. by 3.

Since 15 is the first multiple of 5 that is divisible by 3, the LCM

(3, 5)15.

5, 10, 15, 20, 25,

To find the LCM of two (or more) whole
numbers by listing:

1. Write multiples of the largest number by
   multiplying it by and so on.


2. Continue this process until you find the
   firstmultiple of the larger number that is
   divisible by each of the smaller numbers.
   That multiple is their LCM.

1, 2, 3, 4, 5,

To find the LCM of two (or more) whole
numbers using prime factorization:

1. Prime factor each number.


2. The LCM is a product of prime factors,
   where each factor is used the greatest
   number of times it appears in any one
   factorization.

Find the LCM of 6 and 20.

The greatest number of times 3 appears is once.

The greatest number of times 2 appears is twice.

The greatest number of times 5 appears is once.

Use the factor 2 two times.

Use the factor 3 one time.

Use the factor 5 one time.

LCM (6, 20) 2  2  3  5  60



20  2  2  5

6  2  3

The greatest common factor (GCF)of two (or
more) whole numbers is the largest common
factor of the numbers.

The greatest common factor of two (or more)
numbers is the largest whole number that
divides them exactly.

The factors of 18:

The factors of 30:

The common factors of 18 and 30 are and 6.

The greatest common factor of 18 and 30 is 6, which is written as:

and

30

6

 5

18

6

 3

GCF (18, 30)6.

1, 2, 3,

1 , 2 , 3 , 5, 6 , 10, 15, 30

1 , 2 , 3 , 6, 9 , 18

To find the GCF of two (or more) whole
numbers using prime factorization:

1. Prime factor each number.


2. Identify the common prime factors.


3. The GCF is a product of all the common
   prime factors found in Step 2.

If there are no common prime factors, the
GCF is 1.

Find the GCF of 36 and 60.

36 and 60 have two common factors

of 2 and one common factor of 3.

The GCF is the product of the circled prime factors.

GCF (36, 60) 2  2  3  12

60  2  2  3  5

36  2  2  3  3

 

REVIEW EXERCISES

103. Find the first ten multiples of 9.


104. a. Find the common multiples of 6 and 8 in the
     lists below.
     Multiples of 6:
     Multiples of 8:

b. Find the common factors of 6 and 8 in the lists

below.

Factors of 6:

Factors of 8: 1, 2, 4, 8

1, 2, 3, 6

8, 16, 24, 32, 40, 48, 56, 64, 72 p

6, 12, 18, 24, 30, 36, 42, 48, 54 p

Find the LCM of the given numbers.

105. 
     
     
     
     106. 
          
     
     
     
     


106. 
     
     
     
     108. 
          
     
     
     
     


107. 
     
     
     
     110. 
          
     
     
     
     


108. 
     
     
     
     112. 
          
     
     
     
     

Find the GCF of the given numbers.

113. 
     
     
     
     114. 
          
     
     
     
     


114. 
     
     
     
     116. 
          
     
     
     
     


115. 
     
     
     
     118. 
          
     
     
     
     


116. 48, 72, 120 120.88, 132, 176

63, 84 112, 196

30, 40 30, 45

8, 12 9, 12

4, 14, 20 21, 28, 42

18, 21 24, 45

9, 15 12, 18

4, 6 3, 4

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