Page 235 - Basic College Mathematics with Early Integers

212 C HAPTE R 3 I FRACTIONS

Method 1 for finding multiples works fine for smaller numbers, but may get tedious
for larger numbers. For this reason, let’s study a second method that uses prime
factorization.

Finding the LCD: Method 2
11 7
For example, to find the LCD of and , as in Example 13, let’s look at the prime
12 20
factorization of each denominator.
# #
12 = 2 2 3
# #
20 = 2 2 5
Recall that the LCD must be a multiple of both 12 and 20. Thus, to build the
LCD, we will circle the greatest number of factors for each different prime number.
The LCD is the product of the circled factors.

Prime Number Factors
#
12= 2 2 3
Circle either pair of 2s, but not both.
#
20= 2 2 5

# # #
LCD = 2 2 3 5 = 60
The number 60 is the smallest number that both 12 and 20 divide into evenly. This
method is summarized below:

Method 2: Finding the LCD of a List of Denominators Using
Prime Factorization
Step 1: Write the prime factorization of each denominator.
Step 2: For each different prime factor in Step 1, circle the greatest number of
times that factor occurs in any one factorization.
Step 3: The LCD is the product of the circled factors.

23 17
PRACTICE 14 Example 14 Find the LCD of - and .
72 60
3 11
Find the LCD of - and . Solution: First we write the prime factorization of each denominator.
40 108
# # # #
72 = 2 2 2 3 3
# # #
60 = 2 2 3 5
For the prime factors shown, we circle the greatest number of factors found in
either factorization.
# # # #
72=2 2 2 3 3
# # #
60=2 2 3 5
Copyright 2012 Pearson Education, Inc.
The LCD is the product of the circled factors.
# # # # #
LCD = 2 2 2 3 3 5 = 360
The LCD is 360.

Work Practice 14

Answer
14. 1080