October 07, 2014
How do you find least common
multiple of 2 or more numbers?
October 07, 2014
Guiding Question
How do you skip count by 3s and by 4s?
Skip counting is called multiples.
October 07, 2014
Play Biz Buzz (practice finding multiples)
* everyone sits on their desk
*play by 4 - students count by 4s(multiples of 4)
*first student say 1, second students 2, third 3 and then
fourth says biz buzz (because it is a multiple of 4)
*go around the room and the next student says the next
number, when you get to a multiple of 4 you say biz buzz
* if you say the wrong number you have to sit down and
are out
October 07, 2014
Find the multiples of 3.
How do you know when you find the all?
October 07, 2014
Factors have an ending point and
multiples keep going forever.
factors of 10: 1, 10, 2, 5
multiples of 10: 10,20,30,40,50,60,70, .....
October 07, 2014
Practice
Find the first 5 multiples of each number
1.) 4
2.) 5
3.) 8
October 07, 2014
What does LCM stand for?
October 07, 2014
Example
October 07, 2014
http://www.youtube.com/watch?v=j9PEQP7gpgE
factors and multiples
https://www.youtube.com/watch?v=pQZrkHG2lzc
song
https://learnzillion.com/lessons/799-find-multiples-by-using-a-number-line
extra resource
October 07, 2014
1. List the multiples for both numbers (usually 5-6)
2. circle the ones they have in common
3. take the smallest one
4- 4,8,12,16,20,24
8 - 8,16,24,32,40
LCM of 4 and 8 is 8
October 07, 2014
LCM Dice Game
October 07, 2014
Practice
Find the LCM for each of the following.
1.) 3 and 4
2.) 5 and 4
3.) 9 and 7
4.) 6 and 8
October 07, 2014
Practice - you can do the same process with
3 or more numbers.
Find the LCM for the following.
1.) 3 4 6
2.) 5 3 6
3.) 4 2 3 5
October 07, 2014
Make a connection:
You use the LCM when find the lowest
common denominator (LCD)
Find the LCD for the following fractions:
1. 3/7 and 4/9
2. 4/8 and 2/6
3. 4/5 and 2/4
October 07, 2014
You need to know who to find the LCM for
numbers up to 100.
1.) 45 and 15
2.) 30 and 60
3.) 24 and 48
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http://www.ixl.com/search?q=lcm
IXL practice problems
http://www.fun4thebrain.com/beyondfacts/lcmsnowball.html
game
October 07, 2014
Try
48 and
36
Is using the stagey we have been using beneficial
for this problem?
October 07, 2014
Short cut for finding CGF and LCM using
prime factorization for larger numbers
(optional)
What is a prime and composite
number?
October 07, 2014
Use factor trees to prime
factor these numbers.
16
32
you can use exponents to show solution
October 07, 2014
Practice using factor trees
34
40
81
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https://education-portal.com/member/my-dashboard.html
October 07, 2014
Now use this strategy as a short cut to find
the GCF and LCM of 2 numbers
16
2
32
8
2
4
2 2
16: 2*2*2*2
32: 2*2*2*2*2
8 4
2 4 2 2
2 2
find the largest set of numbers that are the same of each
different number and multiple them together
2*2*2*2*2 = 32 is the LCM
take what is left and multiple 2*2*2*2 = 16 is the GCF
if nothing is left the GCF is 1
October 07, 2014
Another Example
15
3
5
9
3
3
15: 3*5
3*3*5 = 45 LCM
9:
3 = 3 GCF
3*3
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Practice
42
36
63
27
October 07, 2014
How do you use LCM to solve real
world problems?
LCM problems may be asking you :
-­‐about an event that is or will be repea:ng over and over
-­‐to purchase or get mul:ple items in order to have enough
-­‐to figure out when something will happen again at the same :m
October 07, 2014
Example 1:
A radio sta:on is having a promo:on in which every
12th caller receives a free CD and every 20th caller receives
free movie passes. Which caller will be the first one to receive
both prizes?
Discuss the following ques:ons with the students. Have the students work with their shoulder partners to solve this problem.
What do I know?
Every 12th caller receives a free CD and every 20th caller receives free movie passes.
What do I need to know?
Which caller will be the first to receive both prizes?
What is my plan?
This problem can be solved using the Least Common Mul:ple because we are trying to figure out who is the first(Least) to receive both prizes(Mul:ple) it will occur at the same :me (Common).
FInd the LCM for 12 and 20.
List the Mul:ples of each number.
12-­‐ 12, 24, 36, 48, 60
20-­‐ 20, 40, 60
The LCM is 60 and that means that the 60th caller will win both prizes.
October 07, 2014
Example 2:
Desmond is buying two types of paper clips at a local office supply store. The first type comes in packages of 15, whereas the second comes only in packages of 19. If Desmond needs to purchase the same number of each type of paper clip, what is the smallest number of each type that he must buy?
Discuss the following ques:ons with the students.
What do I know?
What do I need to know?
What is my plan?
Find the LCM of 15 and 19 using.
15-­‐ 3 x 5
19-­‐ 1 x 19
3 x 5 x 1 x 19 = 285
The smallest number of paper clips he has to buy is 285.
October 07, 2014
Example 3:
Cody owns a business and assigns two of his employees their shiZs. He assigns the first employee shiZs in blocks of 14 hours, and he assigns the second worker shiZs in blocks of 8 hours. If both workers must receive the same number of hours, what is the minimum number of hours each must be assigned?
October 07, 2014
Task Cards - found on lesson 26 for the
county.
October 07, 2014
http://www.ixl.com/math/grade-6/gcf-and-lcm-word-problems
IXL real world GCF/LCM
October 07, 2014
I can find the LCM or 2 or more
numbers.
October 07, 2014
Post-assessment
1. What are the factors of 16?
2. What are the first 5 multiples of 3?
3. What is the GCF of 12 and 15?
4. What is the LCM of 4 and 6?
October 07, 2014
October 07, 2014