LES
SO
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Least Common Multiple
Goal: Find the least common multiple of two numbers.
Vocabulary
Multiple:
The product of a number and any nonzero whole number.
Common multiple:
A multiple that is shared by two or more
numbers.
Least common multiple (LCM):
EXAMPLE
1
The least of the common multiples
of two or more numbers.
Finding the Least Common Multiple
Inline Skating You and your friend are inline skating around a trail at a
park. You both start skating at the same time from the same location.
You skate the trail in 8 minutes, while your friend skates the trail in
6 minutes. You both stop skating when you both are at your starting
place at the same time again. How long do you and your friend skate?
Method 1: Make a list. List the multiples of each number.
Multiples of 6: 6, 12, 18 , 24 , 30 , 36 , 42, 48, 54, …
Multiples of 8: 8, 16, 24 , 32 , 40 , 48, 56, …
The LCM of 6 and 8 is 24 .
Method 2: Use prime factorization.
Write the prime factorization of each number.
6 2p3
8 23
Write the product of the highest power of each prime number in the prime
factorizations.
23 p 3 24
The LCM of 6 and 8 is 24 .
ANSWER You and your friend skate for 24
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Chapter 4
Notetaking Guide
minutes.
EXAMPLE
2
Finding the Least Common Multiple
Find the LCM of 56, 84, and 112 using prime factorization.
Write the prime factorization of each number.
84 22
56 23 p 7
Hint:
When you are asked to
find the LCM of larger
numbers, it may be
easier to use prime
factorization than to
list the multiples of
each number.
p 3 p7
112 2 4 p 7
Write the product of the highest power of each prime number in the
prime factorizations.
24 p
3 p
7 =
336
ANSWER The LCM of 56, 84, and 112 is 336 .
Y our turn now
Find the least common multiple of the numbers.
1. 4, 10
2. 3, 21
3. 20, 28
20
21
140
EXAMPLE
3
4. 18, 45, 60
180
Finding the LCM of Monomials
Find the LCM of 8a 3bc 2 and 12ac 4.
Factor each expression using exponents.
8a 3bc 2 23 p a 3 p b p c 2
12ac 4 22 p 3 p a p c 4
Find the product of the highest power of each factor, including the variables.
23 p 3 p a 3 p b p c 4
= 24a 3bc 4
ANSWER The LCM of 8a 3bc 2 and 12ac 4 is 24a 3bc 4 .
Y our turn now
5. 12x 5, 16x 8
48x 8
Find the least common multiple of the monomials.
6. 15t 6, 75t
7. 9mn 3, 24m 3n
75t 6
72m 3n 3
Lesson 4.4
Least Common Multiple
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