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2-9 Least Common Multiple
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2-9 Least Common Multiple
Warm Up
Write the prime factorization of each
number.
1. 68
22 · 17
2. 225
32 · 52
3. 940 22 · 5 · 47
Find the greatest common factor.
4. 27 and 45 9
5. 32 and 80
16
2-9 Least Common Multiple
Problem of the Day
Franklin had some counters. When he
counted them by twos, threes, fours,
and fives, he had one left over. If
Franklin had more than 100 and fewer
than 150 counters how many did he
have?
121
2-9 Least Common Multiple
Sunshine State Standards
Prep for MA.7.A.3.2 Add, subtract,
multiply, and divide…fractions…
Review MA.5.A.6.1
2-9 Least Common Multiple
Vocabulary
multiple
least common multiple (LCM)
2-9 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.
2-9 Least Common Multiple
A multiple of a number is a product of that
number and a nonzero 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.
2-9 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.
2-9 Least Common Multiple
Additional Example 1: Using a List to Find the LCM
Find the least common multiple (LCM).
A. 2, 7
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 7: 7, 14, 21, 28, 35
The LCM is 14.
List some multiples of
each number.
Find the least value that
is in both lists.
B. 3, 6, 9
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 6: 6, 12, 18, 24, 30
Multiples of 9: 9, 18, 27, 36, 45
The LCM is 18.
List some multiples of
each number.
Find the least value that
is in all the lists.
2-9 Least Common Multiple
Check It Out: Example 1
Find the least common multiple (LCM).
A. 3, 7
Multiples of 3: 3, 6, 9, 12, 15, 18, 21
Multiples of 7: 7, 14, 21, 28
The LCM is 21.
B. 2, 6, 4
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Multiples of 6: 6, 12, 18
Multiples of 4: 4, 8, 12
The LCM is 12.
List some multiples of
each number.
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.
2-9 Least Common Multiple
Additional Example 2A: Using Prime Factorization to
Find the LCM
Find the least common multiple (LCM).
60, 130
60 = 2 · 2 · 3 · 5
Write the prime factorization of
each number.
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.
2-9 Least Common Multiple
Additional Example 2B: Using Prime Factorization to
Find the LCM
Find the least common multiple (LCM).
14, 35, 49
14 = 2 · 7
35 = 5 · 7
49 = 7 · 7
Write the prime factorization of
each number.
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.
2-9 Least Common Multiple
Check It Out: Example 2A
Find the least common multiple (LCM).
50, 110
50 = 2 · 5 · 5
Write the prime factorization of
each number.
110 = 2 · 5 · 11
Circle the common prime factors.
2, 5, 5, 11
List the prime factors, using
the circled factors only once.
2 · 5 · 5 · 11
Multiply the factors in the list.
The LCM is 550.
2-9 Least Common Multiple
Check It Out: Example 2B
18, 36, 54
18 = 2 · 3 · 3
Write the prime factorization of
each number.
36 = 2 · 2 · 3 · 3
Circle the common prime factors.
54 = 2 · 3 · 3 · 3
2, 2, 3, 3, 3
List the prime factors, using
the circled factors only once.
2·2·3·3·3
Multiply the factors in the list.
The LCM is 108.
2-9 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.
2-9 Least Common Multiple
Check It Out: 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.
72 hours will elapse before they are over the
same location at the same time.
2-9 Least Common Multiple
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
2-9 Least Common Multiple
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
2-9 Least Common Multiple
Lesson Quiz for Student Response Systems
1. Identify the least common multiple (LCM)
of 15 and 24.
A. 105
B. 112
C. 120
D. 124
2-9 Least Common Multiple
Lesson Quiz for Student Response Systems
2. Identify the least common multiple (LCM)
of 21 and 24.
A. 162
B. 168
C. 172
D. 178
2-9 Least Common Multiple
Lesson Quiz for Student Response Systems
3. Identify the least common multiple (LCM)
of 6, 8, and 18.
A. 72
B. 64
C. 56
D. 48
2-9 Least Common Multiple
Lesson Quiz for Student Response Systems
4. Identify the least common multiple (LCM)
of 5, 10, and 20.
A. 25
B. 20
C. 15
D. 10
2-9 Least Common Multiple
Lesson Quiz for Student Response Systems
5. You are planning to distribute pencils,
notebooks, and school bags to children in
an orphanage. You can purchase pencils in
packages of 30, notebooks in packages of
40, and school bags in packages of 50.
What is the least number of each type of
package that you can buy and have an
equal number of each?
A. 20 packages of pencils, 15 packages of
notebooks, and 12 packages of school bags
B. 12 packages of pencils, 15 packages of
notebooks, and 20 packages of school bags