OBJECTIVES

4.1 Least Common Multiples

bSimplify fraction notation like n/n to 1, 0/n to 0, and

n /1 to n.

Slide 1Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

a Find the least common multiple, or LCM, of two ormore numbers.

4.1 Least Common Multiples

a Find the least common multiple, or LCM, of two ormore numbers.

Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

In order to add or subtract fractions, all fractions must share a common denominator.

4.1 Least Common Multiples

aFind the least common multiple, or LCM, of two or

more numbers.

LEAST COMMON MULTIPLE, LCM

Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

The least common multiple, or LCM, of two natural numbers is the smallest number that is a multiple of both numbers.

Title

4.1 Least Common Multiples

aFind the least common multiple, or LCM, of two or

more numbers.

Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Method 1. To find the LCM of a set of numbers using a list of multiples:1. Determine whether the largest number is a multiple of the others. If it is, it is the LCM. That is, if the largest number has the others as factors, the LCM is that number.2. If not, check multiples of the largest number until you get one that is a multiple of each of the others.

Title

4.1 Least Common Multiples

aFind the least common multiple, or LCM, of two or

more numbers.

Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Method. To find the LCM of two numbers using primefactorizations:1. Write the prime factorization of each number.2. Select one of the factorizations and see whether it contains the other.a) If it does, it is the LCM.b) If it does not, multiply that factorization by those prime factors of the other number that it lacks. The final product is the LCM.

Title

4.1 Least Common Multiples

aFind the least common multiple, or LCM, of two or

more numbers.

Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3. As a check, make sure that the LCM includes each factor the greatest number of times that it occurs in either factorization.

EXAMPLE

4.1 Least Common Multiples

a Find the least common multiple, or LCM, of two ormore numbers.

6

Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Find the LCM of 18 and 21.

1. We begin by writing the prime factorization of each number:

EXAMPLE

4.1 Least Common Multiples

a Find the least common multiple, or LCM, of two ormore numbers.

6

Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.1 Least Common Multiples

a Find the least common multiple, or LCM, of two ormore numbers.

12

Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

4.1 Least Common Multiples

a Find the least common multiple, or LCM, of two ormore numbers.

12

Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.