Transcript Gcf lcm - CPalms

The class definition should be typed
in here.
Example: The biggest number that
both numbers can be divided by.
GREATEST COMMON
FACTOR
Word Problems that use GCF …




cut things into smaller sections
equally put 2 or more sets of items into the
largest grouping
ask how many people we can invite
arrange into rows or groups
A GCF word Problem
What questions are we trying to answer?
Jenifer baked 30 brownies and 48 cookies to put
into plastic containers for her friends at school.
She wants to divide the brownies and cookies so
that each container has the same number brownies
and cookies.



What is the least amount of containers she will
need?
How many brownies will be in each container?
How many cookies will be in each container?
What information is needed to find
the answer?

Jenifer has 30 brownies and 48 cookies
And wants to put them into containers that all
have the same amounts of brownies and cookies

GCF - we are dividing both (Common) 30

brownies and 48 cookies into equal
groups(Factor) ,using the most(Greatest) amount
of brownies and cookies each container
Solving GCF:


List 30 (1, 2, 3, 5, 6, 10, 15, 30)
48 (1, 2, 3, 4, 6, 8, 12, 16, 24, 48)
Prime Factorization
48
30
15
3
2
5
4
2
12
2
The factors in common are 2x3
3
4
Now that I know the GCF…




The biggest number I can divide both 30 and 48
into is 6.
I will need 6 containers.
How many brownies in each container?
How many cookies in each container?
USE THE CLASS DEFINITION
FOR LCM HERE
Lowest Common Multiple
LCM Word Problems ask…



events that will be repeating over and over
get multiple items in order to have enough
Find out when something will happen again at the
same time
LCM word Problem
What question are we trying to answer?


Pencils come in packages of 10. Erasers come in
packages of 12. Lily wants to purchase the
smallest number of pencils and erasers so that
she will have exactly 1 eraser per pencil. How
many packages of pencils and erasers should
Lily buy?
What is the smallest number of pencil packs and
eraser packs should Lily buy, so that she will have
exactly 1 eraser per pencil ?
What information do I need to
answer the question?



Pencils come in packages of 10 and erasers in
packages of 12.
How many packages do I need to buy of each until I
have the same amount?
LCM - we are trying to figure out the smallest (Least)
number of pencil packs (10) and eraser packs (12)
(Multiple) to have the same amount of each
(Common)
Solving LCM
List method
10: 10, 20, 30 , 40, 50 , 60 6 packages of 10 pencils=60 pencils
12: 12, 24, 36, 48, 60
5 packages of 12 erasers=60 erasers


Prime factorization
10 ( 2 ,5) and
12 (2, 2, 3)
Prime factors from the largest # 12: ( 2, 2, 3)
include any prime numbers from 10: (5)
2 x 2 x 3 x 5 = 60
Now that I know the LCM…

The smallest amount that I need, is 60 pencils
and 60 erasers, to have exactly one pencil per
eraser .
That means I will need 6 packages of (10) pencils

and 5 packages of (12) erasers .

GCF and LCM



They both deal with the relationship between 2
numbers.
GCF is looking for the greatest factor that
numbers have in common (divide). Taking two
numbers and putting them into equal groups.
LCM is looking for a multiple that two or more
numbers have in common (multiply). Taking the
numbers and continuing a pattern until they
meet.