Download least common multiple (LCM)

5-1 Least Common Multiple
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
5-1 Least Common Multiple
Warm Up
Write the first five multiples of each
number.
1. 5
5, 10, 15, 20, 25
2. 6
6, 12, 18, 24, 30
3. 10
10, 20, 30, 40, 50
4. 12
12, 24, 36, 48, 60
5-1 Least Common Multiple
Problem of the Day
Greg, Sam and Mary all work at the same
high school. One of them is a principal, one
of them is a teacher, and one of them is a
janitor. Sam is older than Mary. Mary does
not live in the same town as the principal.
The teacher, the oldest of the three, often
plays golf with Greg. What is each person’s
job?
Greg, principal; Sam, teacher; Mary, janitor
5-1 Least Common Multiple
Learn to find the least common multiple
(LCM) of a group of numbers.
5-1 Least Common Multiple
Vocabulary
least common multiple (LCM)
5-1 Least Common Multiple
The smallest number that is a multiple of
two or more numbers is the least
common multiple (LCM).
5-1 Least Common Multiple
Find the least common multiple (LCM).
6 and 20
6=2•3
20 = 2
•2•5
Write the prime factorization of
each number.
Line up the common factors.
2•3 •2•5
To find the LCM, multiply one
2 • 3 • 2 • 5 = 60 number from each column.
LCM: 60
5-1 Least Common Multiple
Find the least common multiple (LCM).
Use a list.
4, 5, and 8
4: 4, 8, 12 , 16, 20, 24, 28, 32,
36, 40, 44, . . .
List multiples of 4, 5, and 8.
5: 5, 10, 15, 20, 25, 30, 35, 40,
45, . . .
8: 8, 16, 24, 32, 40, 48, . . .
LCM: 40
Find the smallest number
that is in all the lists.
5-1 Least Common Multiple
Find the least common multiple (LCM).
15, 6, and 4
15 = 3 • 5
6=3•
2
4=
22
3 • 5 • 22
3 • 5 • 22 = 60
LCM: 60
Write the prime factorization of
each number in exponential form.
To find the LCM, multiply each
prime factor once with the
greatest exponent used in any of
the prime factorizations.
5-1 Least Common Multiple
English muffins come in packs of 8, and eggs come in
cartons of 12. If there are 24 students, what is the least
number of packs and cartons needed so that each
student has a muffin sandwich with one egg and there
are none left over?
Draw muffins in groups of 8. Draw eggs in groups of 12.
Stop when you have drawn the same number of each.
There are 24 English muffins and 24 eggs.
So 3 packs of English muffins and 2 cartons of eggs are
needed.
5-1 Least Common Multiple
Dog cookies come in packages of 6, and bones in bags of
9. If there are 18 dogs, what is the least number of
packages and bags needed so that each dog has a treat
box with one bone and one cookie and there are no
bones or cookies left over?
Draw cookies in groups of 6. Draw bones in groups of 9. Stop
when you have drawn the same number of each.
There are 18 dog cookies and 18 bones.
So 3 packages of dog cookies and 2 bags of bones are needed.
5-1 Least Common Multiple
Hot dogs come in packs of 8. Hot dog
rolls come in packs of 12.
What is the least number of packs of
each you need to have
enough to serve 24 people and have
none left over?
5-1 Least Common Multiple
Invitations come in packs of 12 and
stamps come in sheets of 10.
What is the least number of each you
need to invite 60 people and
have no stamps or invitations left
over?
5-1 Least Common Multiple
Find the least common multiple (LCM).
3, 4, and 9
3: 3, 6, 9, 12, 15, 18, 21, 24,
27, 30, 33, 36, . . .
List multiples of 3, 4, and 9.
4: 4, 8, 12, 16, 20, 24, 28, 32,
36, …
Find the smallest number
that is in all the lists.
9: 9, 18, 27, 36, 45, . . .
The least common multiple of 3, 4, and 9 is 36.
5-1 Least Common Multiple
Find the least common multiple (LCM).
4 and 10
4=2•2
10 = 2
•5
Write the prime factorization of
each number.
Line up the common factors.
2•2 •5
2 • 2 • 5 = 20
LCM: 20
To find the LCM, multiply one
number from each column.
5-1 Least Common Multiple
Find the least common multiple (LCM).
12, 6, and 8
12 = 22 • 3
6=2• 3
Write the prime factorization of
each number in exponential form.
8 = 23
23 • 3
23 • 3 = 24
LCM: 24
To find the LCM, multiply each
prime factor once with the
greatest exponent used in any of
the prime factorizations.
5-1 Least Common Multiple
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
5-1 Least Common Multiple
Lesson Quiz
Find the least common multiple (LCM).
1. 6, 14 42
2. 9, 12 36
3. 5, 6, 10 30
4. 12, 16, 24, 36
144
5. Two students in Mrs. Albring’s preschool class are
stacking blocks, one on top of the other. Reece’s
blocks are 4 cm high, and Maddy’s blocks are 9 cm
high. How tall will their stacks be when they are
the same height for the first time?
36 cm
5-1 Least Common Multiple
Lesson Quiz for Student Response Systems
1. Identify the least common multiple (LCM).
8, 18
A. 144
C. 72
B. 120
D. 64
5-1 Least Common Multiple
Lesson Quiz for Student Response Systems
2. Identify the least common multiple (LCM).
9, 24
A. 72
C. 52
B. 64
D. 27
5-1 Least Common Multiple
Lesson Quiz for Student Response Systems
3. Identify the least common multiple (LCM).
3, 15, 18
A. 94
C. 54
B. 90
D. 24
5-1 Least Common Multiple
Lesson Quiz for Student Response Systems
4. Identify the least common multiple (LCM).
9, 12, 18, 27
A. 108
C. 172
B. 144
D. 216
5-1 Least Common Multiple
Lesson Quiz for Student Response Systems
5. Water colors come in boxes of 6 and brushes
come in packets of 10. Tom wants to give
each of 30 students a water color and a
brush. What is the least number of boxes and
packs he should buy so there are none left
over?
A. 3 boxes of water colors and 5 packs of brushes
B. 5 boxes of water colors and 3 packs of brushes
C. 4 boxes of water colors and 2 packs of brushes
D. 2 boxes of water colors and 4 packs of brushes