Transcript Factors and Multiples

Warm Up
Using the ladder method, find the GCF
of these numbers:
1. 36
48
2. 24
30
3. 30
45
What am I Learning Today?
LCM
How will I show that I learned it?
Use multiples to uncover hidden picture
Determine the GCF and LCM using the list and
ladder method
Vocabulary
Common multiple: multiples shared by two
or more whole numbers.
Least Common Multiple (LCM): The smallest
nonzero number that is a multiple of two or
more numbers.
What is the least
common multiple?
The smallest number that is a multiple of two
or more numbers
How do I find the LCM?
Using the list method or the ladder
How do I use the list
method?
1. List all the multiples for those two numbers.
2. Circle the smallest multiple that they share.
List the LCM for 5 and 8.
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, . .
8: 8, 16, 24, 32, 40, 48, . . .
How do I use the ladder
method?
LCM: 40
1. Begin with a factor that divides into each
number evenly.
2. Keep dividing until there are no more common
factors.
3. Find the product of all of the numbers on the
outside of the ladder (LCM is ALL OF THEM).
Using the ladder, find the
LCM for 40 and 16.
What happens if I have
two numbers that do not
have a common factor
other then one?
2 40 16
2 20 8
2 10 4
5 2
2 • 2 • 2 • 2 • 5 = 80
Simply multiply the two numbers together and
that IS the LCM
“GCF is on the left
LCM is all of them”
Find the Least Common Multiple
Use BOTH the list and ladder method in order to
check your answers.
LCM of 32 and 24
2
Multiples of 32: 32, 64, 96, 128, 160
Multiples of 24: 24, 48, 72, 96, 120
LCM of 54 and 36
Multiples of 54: 54, 108, 113, 216
Multiples of 36: 36, 72, 108, 144
32
24
2 16
12
2
2
8
6
4
3
54
3
36
27
18
3 9
3
“GCF is on the left
6
2
LCM is all of them”
Find the GCF AND LCM of 30 and 40
2 30 40
5 15 20
3
GCF
2 • 5 = 10
4
LCM
2 • 5 • 3 • 4 = 120
“GCF is on the left
LCM is all of them”
Find LCM using a Venn
Diagram
Paired Discussion
Turn to a partner and discuss the following:
Why can’t you find the Greatest Common
Multiple for a group of numbers?
Multiples go on indefinitely, so there is no possible way to
find the GREATEST common multiple.
Can the LCM of a set of numbers ever be
smaller than any of the numbers
in the set? Explain.
No. It can be equal to one of the
numbers, but never smaller. Multiples are
products and the smallest one is the
identity property which is unique to each
number.