Transcript GCF and LCM - SchoolNotes

How do you find them?
 At the beginning of the summer, Lauren had a balance $25
in her bank account. She saved a total of $145 from her
summer job, which she deposited into her account. Today
Lauren withdrew enough money from her account to cover
her $20 athletic facilities fee and her $30 uniform fee. If
Lauren made no other withdrawals or deposits, what is her
account balance?
The balance of Lauren’s account is $120.
 Starting today, Lauren will earn $20 each week in
allowance, which she plans to deposit into her bank
account. If Lauren makes no other withdrawals or deposits,
after how many weeks will the balance in her bank account
be double what it is now?
Her account will double in 6 weeks.
Warm-Up
1.
What is the prime factorization of 48?
Prime Factorization of 24:
2•2•2•23
2. What is the GCF of 35, 21, and 84?
The GCF of 35, 21, and 84 is 7.
Warm-Up
1.
Find the GCF of 28 and 42 using prime factorization.
28 = 2  2  7 and 42 = 2  3  7
The GCF of 28 and 42 is 14.
1.
What is the LCM of 12 and 32?
The LCM of 12 and 32 is 96.
What is a factor?
2 and 3 are both
factors of 6. What
are the other
factors of 6?
What is a prime number?
 Numbers that have no other factors but itself and one!
 What are the first 6 prime numbers?
2, 3, 5, 7, 11, 13
What is prime factorization?
 The prime numbers that multiply together to get the
original number.
Use the ladder method!
Begin with the lowest prime number and see if it is
divisible by the original number.
2. Continue until it is no longer divisible by that
number, then move on to the next prime number
3. Continue dividing by prime numbers until the only
number left inside the ladder is one
1.
 What is the prime factorization of 24?
2 24
2 12
2 6
3
3
Prime Factorization
of 24:
2•2•2•3
1
 What is the prime factorization of 39?
3 39
13 13
1
Prime Factorization
of 39:
3•13
What is the Greatest Common Factor?
 It is the largest of the common factors between
two numbers.
Method 1: Rainbow!
 What is the greatest common factor of 16 and 36?
 16: 1, 2, 4, 8, 16
 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The greatest common
factor or 16 and 36 is 4.
List all the factors of each
of the numbers. Once you
either have 2 of the same
factors or numbers that
are so close there are no
other factors between
them, then you’ve reached
the middle of the rainbow.
Method 2: Find each number’s prime
factorization
 What is the greatest common factor of 12 and 18?
2 18
3 9
What do
3 3
they have in
1
common?
2 12
2 6
33
1
2•2•3
2•3=6
2•3•3
The greatest common
factor of 12 and 18 is 6.
What is the greatest common factor of
28 and 35?
 Use both methods
 28: 1, 2, 4, 7, 14, 28
 35: 1, 5, 7, 35
2 28
2 14
77
1
2•2•7
Using the rainbow
method, the GCF is 7.
5 35
7 7
1
5•7
Using the prime
factorization method, the
GCF is 7.
Warm-Up
What is a multiple?
 The number you get when you multiply a number by
another number
What are the multiples of 5?
5, 10, 15, 20,
25, 30…
What is the least common multiple?
 It is the smallest multiple that is shared between two
numbers.
How to find LCM
It’s simple…Just list the multiples of each number
until you find one that is in common!
What is the LCM of 4 and 7?
4: 4, 8, 12, 16, 20, 24, 28
7: 7, 14, 21, 28
What is the LCM of 12 and 16?
12: 12, 24, 36, 48
16: 16, 32, 48
Which should you use to solve the
problem, GCF or LCM?
 Two shuttles leave the Hard Rock Hotel to go to
Universal Studios at the same time. The Minion
Madness shuttle returns to the hotel every 8 minutes.
The Incredible Hulk shuttle returns to the hotel every
10 minutes. In how many minutes will Minion
Madness and the Incredible Hulk leave the hotel
together for the second time?
Use the
LCM!
The shuttles will leave the hotel
at the same time in 40 minutes.
Which should you use to solve the
problem, GCF or LCM?
 Mr. Schuester directs two show choirs. One choir has
28 students. The other choir has 36 students. For
rehearsals, he wants to divide each chorus into the
largest possible equal groups with no students left
over. How many students will be in each group?
Use the
GCF!
Mr. Schuester can divide each
choir into groups of 4.
Warm-Up
Let’s have Tim and Moby gives us the basics. :)
http://www.brainpop.com/math/numbersandoperations/distri
butiveproperty/
How does the distributive property work?
The number outside the
parentheses “jumps”
over the parentheses
and multiplies by each
number inside!
Just bring down the
sign!
Multiply and then
add!
2(2 + 3)
(2 • 2) + (2 • 3)
(4) + (6)
=10
You can write a number or sum in
distributive form…
 How can you write an expression equal to 33 + 77 using
distributive form?
1. Find the GCF of the two numbers. (This will go outside
of the parentheses.)

GCF: 11

11()
2. Now use the other factor that multiplies with the GCF
to get the original number. (Those 2 numbers go inside
of the parentheses.)

3 • 11 & 7 • 11

11(3 + 7)
Now you try one!
 The number 108 can be expressed as the sum 100 + 8.
How can you use the distributive property to rewrite
that sum as a multiple of a sum whose addends have
no common factors? (Tip: Ignore all the crazy wording
and just figure out what’s important!)
4(25 + 2)