Transcript 5.1 Least Common Multiple Power Point

5-1 Least Common Multiple
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
5-1 Least Common Multiple
Do Now
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
Objective
SWBAT find the least common multiple
(LCM) of a group of numbers using two
methods.
5-1 Least Common Multiple
Vocabulary
least common multiple (LCM)
5-1 Least Common Multiple
Remember!
A multiple of a number is the
product of the number and any
nonzero whole number.
5-1 Least Common Multiple
Ex. 1 Consumer Application
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
Try this one on your own…
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
Try this one on your own…
Hotdogs come in packages of 10, and buns come
packages of 8. If you are throwing a BBQ party and
want to serve hotdogs with buns, what is the least
amount of hotdogs and buns you would have to buy so
that there are no remaining hotdogs and buns?
5-1 Least Common Multiple
The smallest number that is a multiple of
two or more numbers is the least
common multiple (LCM). In Additional
Example 1, the LCM of 8 and 12 is 24.
5-1 Least Common Multiple
Ex. 2 - Using Multiples to Find the LCM
Find the least common multiple (LCM).
Method 1: 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
Remember!
The prime factorization of a number is
the number written as a product of its
prime factors.
5-1 Least Common Multiple
Ex. 3 - Using Multiples to Find the LCM
Find the least common multiple (LCM).
Method 2: Use prime factorization.
6 and 20
1-2 Divide Multi-Digit Whole Numbers
1.) What is the prime factorization of each
number?
2.) Did I line up the factors from least to greatest?
3.) Did I use the exponent from each factor?
4.) Did I multiply?
1-2 Divide Multi-Digit Whole Numbers
Ex. 3 - Using Multiples to Find the LCM
Find the least common multiple (LCM).
Method 2: Use prime factorization.
6 and 20
1.) What is the prime factorization
of each number?
2.) Did I line up the factors from
least to greatest?
3.) Did I exponent from each
factor?
4.) Did I multiply?
5-1 Least Common Multiple
Ex. 4
Find the least common multiple (LCM).
15, 6, and 4
1.) What is the prime factorization
of each number?
2.) Did I line up the factors from
least to greatest?
3.) Did I exponent from each
factor?
4.) Did I multiply?
5-1 Least Common Multiple
Try this one on your own… (Use a list)
Find the least common multiple (LCM).
3, 4, and 9
5-1 Least Common Multiple
Try this one on your own… (Use prime factorization)
Find the least common multiple (LCM).
4 and 10
5-1 Least Common Multiple
Try this one on your own… (Use any method you desire)
Find the least common multiple (LCM).
12, 6, and 8
5-1 Least Common Multiple
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
5-1 Least Common Multiple
Exit Ticket
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