LES
SO
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Least Common Multiple
Goal: Find the LCM of two or more numbers.
Vocabulary
Multiple:
A multiple of a number is the product of the number
and any nonzero whole number.
Common multiple:
A multiple that is shared by two or more
numbers is a common multiple.
Least common multiple:
EXAMPLE
1
The least of the common multiples is the
least common multiple.
Using the Least Common Multiple
Commercials One TV station shows commercials every 6 minutes. Another
station shows commercials every 8 minutes. For the shows that air at
7:00 A.M., at what time will both stations first play a commercial?
You can determine when both stations will first play a commercial by finding
the least common multiple of 6 and 8. Begin by writing the multiples of
6 and 8. Then identify any common multiples.
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, . . .
Multiples of 8:
8, 16, 24, 32, 40, 48 , . . .
24 and 48 are
common multiples.
The LCM is 24 .
Answer: The television stations will first both show a commercial in
24 minutes, or at 7:24
EXAMPLE
2
A.M.
Finding the Least Common Multiple
Find the least common multiple of 5 and 9.
Multiples of 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . .
Multiples of 9:
9, 18, 27, 36, 45, 54, . . .
Answer: The least common multiple of 5 and 9 is 45 .
Lesson 4.4
Least Common Multiple
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3
EXAMPLE
Use the prime
factorization method
to find the least
common multiple
of large numbers.
Using Prime Factorization to Find the LCM
Find the LCM of 95 and 240 using prime factorization.
1. Begin by writing the prime factorization of each number.
95
240
5 19
10 24
2 5 4 6
2 5 2 2 2 3
95:
240:
5 19
222235
2. Circle the common factor. Then multiply the common factor and all the
uncircled factors.
2 2 2 2 3 5 19 4560
Answer: The least common multiple of 95 and 240 is 4560 .
Guided Practice
Find the LCM of the numbers by listing the multiples.
1. 4, 7
2. 10, 15
28
3. 3, 8, 12
4. 2, 6, 10
24
82
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Chapter 4
Notetaking Guide
30
30
Guided Practice
Find the LCM of the numbers using prime factorization.
5. 42, 70
6. 18, 27
210
54
7. 15, 20, 40
8. 45, 60, 72
120
EXAMPLE
4
360
Using the Least Common Multiple
Fitness Center All classes at the fitness center start at 6 A.M. The water
aerobics class repeats every 60 minutes. The power yoga class repeats
every 45 minutes. The circuit training class repeats every 90 minutes.
What is the next time that all three classes start at the same time?
Solution
Find the least common multiple of 60, 45, and 90.
60 2 2 3 5
45 32 5
90 2 3 2 5
2
2
The least common multiple is 2 3 5 180 .
Answer: The classes start at the same time again in 180
3 hours, after 6 A.M., which is 9
minutes, or
A.M.
Lesson 4.4
Least Common Multiple
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