Transcript Tuesday, Oct 30

5 Minute Check
Find the GCF. (On back of homework)
1. 8, 14
2. 21, 35, 49
3. A gardener has 27 roses and 36 daisies. He
plants an equal number of each type of flower in
each row. What is the greatest possible number
of roses in each row?
5 Minute Check
Find the GCF.
1. 8, 14
8; 1, 2, 4, 8
14;, 1, 2, 7, 14
2.
21, 35, 49
3. A gardener has 27 roses and 36 daisies. He
plants an equal number of each type of flower in
each row. What is the greatest possible number
of roses in each row?
5 Minute Check
Find the GCF.
1. 8, 14
8; 1, 2, 4, 8
14;, 1, 2, 7, 14
2. 21, 35, 49
21; 1, 3, 7, 21
35; 1, 5, 7, 35
49; 1, 7, 49
3. A gardener has 27 roses and 36 daisies. He
plants an equal number of each type of flower in
each row. What is the greatest possible number
of roses in each row?
5 Minute Check
Find the GCF.
1. 8, 14
8; 1, 2, 4, 8
14;, 1, 2, 7, 14
2. 21, 35, 49
21; 1, 3, 7, 21
35; 1, 5, 7, 35
49; 1, 7, 49
3. A gardener has 27 roses and 36 daisies. He
plants an equal number of each type of flower in
each row. What is the greatest possible number
of roses in each row?
27: 1,3,9,27
36:1,2,3,4,6,9,12,18,36
Wednesday, Sept 4
Lesson 1.1a
Least Common Multiple
Factors and Multiples
Objective: To find the Least Common
Multiple.
Factors and Multiples
Factors and Multiples
The least number that is a multiple of two or
more whole numbers is the least common
multiple (LCM) of the numbers.
Page 7
Factors and Multiples
Least Common Multiple–
What does “least” mean?
Factors and Multiples
Least Common Multiple–
What does “common” mean?
Factors and Multiples
Least Common Multiple–
What does “multiple” mean?
Factors and Multiples
Least Common Multiple would be the smallest
number that is in all multiple lists.
Factors and Multiples
There are two ways to find the LCM.
-Multiples List
-Factor Trees
Factors and Multiples
Find the LCM of 2 and 3.
Factors and Multiples
Find the LCM of 2 and 3.
Multiples List Method
Step 1 – List the multiples for each number.
(Create a multiples list)
Factors and Multiples
Find the LCM of 2 and 3.
Step 1 – List the multiples for each number.
(Create a multiples list)
2; 2, 4, 6, 8, 10…..
Factors and Multiples
Find the LCM of 2 and 3.
Step 1 – List the multiples for each number.
(Create a multiples list)
2; 2, 4, 6, 8, 10…..
3; 3, 6, 9, 12, 15…..
Factors and Multiples
Find the LCM of 2 and 3.
2; 2, 4, 6, 8, 10…..
3; 3, 6, 9, 12, 15…..
Step 2 – Determine the smallest number that
is in each list.
Factors and Multiples
Find the LCM of 2 and 3.
2; 2, 4, 6, 8, 10…..
3; 3, 6, 9, 12, 15…..
Step 2 – Determine the smallest number that
is in each list.
The LCM of 2 and 3 is 6.
Factors and Multiples
Find the LCM of 2 and 6.
Step 1 ?
Factors and Multiples
Find the LCM of 2 and 6.
2; 2, 4, 6, 8, 10…..
Factors and Multiples
Find the LCM of 2 and 6.
2; 2, 4, 6, 8, 10…..
6; 6, 12, 18, 24…..
Step 2?
Factors and Multiples
Find the LCM of 2 and 6.
2; 2, 4, 6, 8, 10…..
6; 6, 12, 18, 24…..
The LCM of 2 and 6 is 6.
Factors and Multiples
Mr. Avery’s LCM Rule – If the smaller
number goes into the larger number(s), the
larger number is the LCM.
Since 2 x 3 = 6, the LCM of 2 and 6 is 6.
.
Factors and Multiples
Find the LCM of 4, 5 and 10.
Step 1 ?
Factors and Multiples
Find the LCM of 4, 5 and 10.
4; 4, 8, 12, 16, 20 , 24….
5; 5, 10, 15, 20, 25…..
10; 10, 20, 30 ……
Step 2?
Factors and Multiples
Find the LCM of 4, 5 and 10.
4; 4, 8, 12, 16, 20 , 24….
5; 5, 10, 15, 20, 25…..
10; 10, 20, 30 ……
The LCM of 4, 5, and 10 is 20.
Factors and Multiples
Find the LCM of 12 and 15.
Factor Tree Method
Factors and Multiples
Find the LCM of 12 and 15.
Factor Tree Method
Step 1 – Create a factor tree for each
number.
12
15
/ \
/ \
2 x 6
3 x 5
I
/ \
2 x 2 x 3
Factors and Multiples
Find the LCM of 12 and 15.
12
15
/ \
/ \
2 x 6
3 x 5
I
/ \
2 x 2 x 3
Step 2 – Make a Venn Diagram with the
prime factors.
Factors and Multiples
Find the LCM of 12 and 15.
12 = 2 x 2 x 3
15 = 3 x 5
12
5
2
2
3
15
Factors and Multiples
Find the LCM of 12 and 15.
Step 3 – Multiply ALL the numbers
inside the Venn Diagram.
12
3
2
2
5
15
Factors and Multiples
Find the LCM of 12 and 15.
The LCM is 60 (2 x2x3x5)
12
3
2
2
5
15
Factors and Multiples
Find the LCM of 3, 5 and 7.
(Do this on your own)
Factors and Multiples
Find the LCM of 3, 5 and 7.
3; 3, 6, 9, 12, 15, 18, …..
5; 5, 10, 15, 20, ……
7; 7, 14, 21, 28, 35, ……
Factors and Multiples
Find the LCM of 3, 5 and 7.
Mr. Avery’s Second LCM Rule – If all the
numbers are prime, the LCM is the product
of those numbers.
Since 3, 5, and 7 are prime, the LCM is the
product. The LCM is 105 (3 x 5 x 7)
Factors and Multiples
Find the LCM of 9, 12 and 18.
(Do this on your own)
Factors and Multiples
Find the LCM of 9, 12 and 18.
9; 9, 18, 27, 36, 45, 54……
12; 12, 24, 36, 48……
18; 18, 36, 54, 72……
The LCM of 9, 12, and 18 is 36.
Factors and Multiples
Find the LCM of 5, 10 and 15.
(Do this on your own)
Factors and Multiples
Find the LCM of 5, 10 and 15.
5; 5, 10, 15, 25, 30, 35, 40……
10; 10, 20, 30, 40……
15; 15, 30, 45, 60……
The LCM of 5, 10, and 15 is 30.
Factors and Multiples
Ernesto has painting class every 2 weeks. Kamala has
pottery class every 5 weeks. Ernesto and Kamala met at
the art building for class this week. How many weeks will it
be before they see each other again?
(Do this on your own)
Factors and Multiples
Ernesto has painting class every 2 weeks. Kamala has
pottery class every 5 weeks. Ernesto and Kamala met at
the art building for class this week. How many weeks will it
be before they see each other again?
2; 2, 4, 6, 8, 10, 12, 14…….
5; 5, 10, 15, 20…….
They will see each other again in 10 weeks.
OAA Review
At Stone Middle School, the band has a concert every 4
weeks and the drama club has a play every 6 weeks. Both
groups performed during the first week of school. When is
the next time they will perform in the same week?
OAA Review
At Stone Middle School, the band has a concert every 4
weeks and the drama club has a play every 6 weeks. Both
groups performed during the first week of school. When is
the next time they will perform in the same week?
4; 4, 8, 12, 16, 20, 24, 28…..
6; 6, 12, 18, 24, 30, 36………
They will perform together again the 12th week of school.
OAA Review
Buses to the stadium leave Central Station every 10
minutes. Buses to the zoo leave Central Station every
16 minutes. Both buses leave Central Station at 4PM.
When is the next time both buses will leave at the same
time?
OAA Review
Buses to the stadium leave Central Station every 10
minutes. Buses to the zoo leave Central Station every
16 minutes. Both buses leave Central Station at 4PM.
When is the next time both buses will leave at the same
time?
10; 10, 20, 30, 40, 50, 60, 70, 80, 90, 100…..
16; 16, 32, 48, 64, 80, 96………
They will leave at the same time 80 minutes later, which is
5:20PM.
OAA Review
Ms. Mason is packaging science supplies for a group of
students. She has 40 hand lenses, 32 pairs of tweezers,
and 28 pens. She want to package the supplies so that
every group has the same number of each item. What is
the greatest number of packages she can make without
having leftover items?
OAA Review
Ms. Mason is packaging science supplies for a group of
students. She has 40 hand lenses, 32 pairs of tweezers,
and 28 pens. She want to package the supplies so that
every group has the same number of each item. What is
the greatest number of packages she can make without
having leftover items?
40; 1, 2, 4, 5, 8, 10, 20, 40
32; 1, 2, 4, 8, 16, 32
28; 1, 2, 4, 7, 14, 28
OAA Review
Ms. Mason is packaging science supplies for a group of
students. She has 40 hand lenses, 32 pairs of tweezers,
and 28 pens. She want to package the supplies so that
every group has the same number of each item. What is
the greatest number of packages she can make without
having leftover items?
40
/ \
2 x 10
I
/ \
2 x 2 x 5
32
/ \
2 x 16
I
/ \
2 x 2 x 8
I
I / \
2 x 2 x 2 x 4
I I
I / \
2 x 2 x 2 x 2 x 2
28
/ \
2 x 14
I
/ \
2 x 2 x 7
OAA Review
Ms. Mason is packaging science supplies for a group of
students. She has 40 hand lenses, 32 pairs of tweezers,
and 28 pens. She want to package the supplies so that
every group has the same number of each item. What is
the greatest number of packages she can make without
having leftover items?
40
2 2
32
To find the GCF
we multiply the numbers
5
2
2
in the intersection.
2x2=4
2
28
7
Factors and Multiples
Agenda Notes
Homework –
Homework Practice 1-1a
Due Thursday, Sept 5