Download Find the least common multiple

2-6 Least Common Multiple
Learn to find the least common multiple
of two or more whole numbers.
Course 2
2-6 Least
InsertCommon
Lesson Title
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Multiple
Vocabulary
multiple
least common multiple (LCM)
Course 2
2-6 Least Common Multiple
The maintenance schedule on Ken’s pickup
truck shows that the tires should be rotated
every 7,500 miles and that the oil filter should
be replaced every 5,000 miles. What is the
lowest mileage at which both services are due
at the same time? To find the answer you can
use least common multiples.
Course 2
2-6 Least Common Multiple
A multiple of a number is a product of that
number and a whole number. Some
multiples of 7,500 and 5,000 are as follows:
7,500: 7,500, 15,000, 22,500, 30,000, 37,500, 45,000, . . .
5,000: 5,000, 10,000, 15,000, 20,000, 25,000, 30,000, . . .
A common multiple of two or more numbers
is a number that is a multiple of each of the
given numbers. So 15,000 and 30,000 are
common multiples of 7,500 and 5,000.
Course 2
2-6 Least Common Multiple
The least common multiple (LCM) of two
or more numbers is the common multiple
with the least value. The LCM of 7,500 and
5,000 is 15,000. This is the lowest mileage
at which both services are due at the same
time.
Course 2
2-6 Least Common Multiple
Additional Example 1: Using a List to Find the LCM
Find the least common multiple (LCM).
A. 2, 7
2: 2, 4, 6, 8, 10, 12, 14 List some multiples of each
number.
7: 7, 14, 21, 28, 35
The LCM is 14.
B. 3, 6, 9
3: 3, 6, 9, 12, 15, 18, 21
6: 6, 12, 18, 24, 30
9: 9, 18, 27, 36, 45
The LCM is 18.
Course 2
Find the least value that is
in both lists.
List some multiples of each
number.
Find the least value that is
in all the lists.
2-6 Least Common Multiple
Additional Example 2A: Using Prime Factorization to
Find the LCM
Find the least common multiple (LCM).
A. 60, 130
60 = 2 · 2 · 3 · 5
130 = 2 · 5 · 13
Circle the common prime factors.
2, 2, 3, 5, 13
List the prime factors, using
the circled factors only once.
2 · 2 · 3 · 5 · 13
Multiply the factors in the list.
The LCM is 780.
Course 2
Write the prime factorization of
each number.
2-6 Least Common Multiple
Additional Example 2B: Using Prime Factorization to
Find the LCM
Find the least common multiple (LCM).
B. 14, 35, 49
14 = 2 · 7
35 = 5 · 7
49 = 7 · 7
Circle the common prime factors.
2, 5, 7, 7
List the prime factors, using
the circled factors only once.
2·5·7·7
Multiply the factors in the list.
The LCM is 490.
Course 2
Write the prime factorization of
each number.
2-6 Least Common Multiple
Additional Example 3: Application
Mr. Washington will set up the band chairs all
in rows of 6 or all in rows of 8. What is the
least number of chairs he will set up?
Find the LCM of 6 and 8.
6=2·3
8=2·2·2
The LCM is 2 · 2 · 2 · 3 = 24.
He will set up at least 24 chairs.
Course 2
2-6 Insert
Lesson Title
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Least Common
Multiple
Try This: Example 3
Two satellites are put into orbit over the same
location at the same time. One orbits the earth
every 24 hours, while the second completes an
orbit every 18 hours. How much time will
elapse before they are once again over the
same location at the same time?
Find the LCM of 24 and 18.
24 = 2 · 2 · 2 · 3
18 = 2 · 3 · 3
The LCM is 2 · 2 · 2 · 3 · 3 = 72.
Course 2
2-6 Least
InsertCommon
Lesson Title
Multiple
Here
Lesson Quiz
Find the least common multiple (LCM).
1. 18, 21
126
2. 24, 27
3. 4, 6, 15
60
4. 4, 8, 16 16
216
5. You are planning a picnic. You can purchase
paper plates in packages of 30, paper napkins in
packages of 50, and paper cups in packages of
20. What is the least number of each type of
package that you can buy and have an equal
number of each?
10 packages of plates
6 packages of napkins
15 packages of cups
Course 2