Gcf and lcm (1)

Real Life Applications ofReal Life Applications of
GCF and LCMGCF and LCM
How can you tell if a word problem requires youHow can you tell if a word problem requires you
to useto use
Greatest Common FactorGreatest Common Factor
or Least Common Multipleor Least Common Multiple
to solve?to solve?

GCF and LCMGCF and LCM
Problem SolvingProblem Solving
First, use ourFirst, use our
PROBLEM SOLVING PROCESSPROBLEM SOLVING PROCESS
 What do I know?What do I know?
 What do I need toWhat do I need to
know?know?
 What is my plan?What is my plan?

GCF ProblemsGCF Problems
may be asking you:may be asking you:
 to split things into smallerto split things into smaller
sections?sections?
 to equally distribute 2 orto equally distribute 2 or
more sets of items into theirmore sets of items into their
largest grouping?largest grouping?
 to figure out how manyto figure out how many
people we can invite?people we can invite?
 to arrange something intoto arrange something into
rows or groups?rows or groups?

GCF ExampleGCF Example
 Samantha has two pieces of cloth.Samantha has two pieces of cloth.
One piece is 72 inches wide and theOne piece is 72 inches wide and the
other piece is 90 inches wide. Sheother piece is 90 inches wide. She
wants to cut both pieces into stripswants to cut both pieces into strips
of equal width that are as wide asof equal width that are as wide as
possible. How wide should she cutpossible. How wide should she cut
the strips?the strips?

Samantha has two pieces of cloth. OneSamantha has two pieces of cloth. One
piece is 72 inches wide and the otherpiece is 72 inches wide and the other
piece is 90 inches wide. She wants topiece is 90 inches wide. She wants to
cut both pieces into strips of equalcut both pieces into strips of equal
width that are as wide as possible. Howwidth that are as wide as possible. How
wide should she cut the strips?wide should she cut the strips?
The pieces of cloth are 72 and 90The pieces of cloth are 72 and 90
inches wide.inches wide.
 What do I need to find out?What do I need to find out?
How wide should she cut the stripsHow wide should she cut the strips
so that they are the largestso that they are the largest
possible equal widths.possible equal widths.

This problem can be solved usingThis problem can be solved using
Greatest Common FactorGreatest Common Factor
because we are cutting or “dividing”because we are cutting or “dividing”
the strips of cloth into smallerthe strips of cloth into smaller
piecespieces ((FactorFactor)) of 72 and 90of 72 and 90
((CommonCommon)) and we are looking forand we are looking for
the widest possible stripsthe widest possible strips
((GreatestGreatest).).
 I will find the GCF of 72 and 90I will find the GCF of 72 and 90
Samantha has two pieces of cloth. OneSamantha has two pieces of cloth. One
piece is 72 inches wide and the otherpiece is 72 inches wide and the other
piece is 90 inches wide. She wants topiece is 90 inches wide. She wants to
cut both pieces into strips of equalcut both pieces into strips of equal
width that are as wide as possible. Howwidth that are as wide as possible. How
wide should she cut the strips?wide should she cut the strips?

GCF Word Problem SolutionGCF Word Problem Solution
GCF using ‘List Method”GCF using ‘List Method”
8 x 98 x 9 9 x 109 x 10
6 x 126 x 12 6 x 156 x 15
4 x4 x 1818 5 x5 x 1818
3 x 243 x 24 3 x 303 x 30
2 x 362 x 36 2 x 452 x 45
1 x 721 x 72 1 x 901 x 90
GCF using “Common Prime Factors Method”GCF using “Common Prime Factors Method”
72 =72 = 22 x 2 x 2 xx 2 x 2 x 33 xx 33
90 =90 = 22 xx 33 xx 33 x 5x 5
GCF = 2 x 3 x 3 = 18GCF = 2 x 3 x 3 = 18
Samantha should cut each piece to be 18Samantha should cut each piece to be 18
inches wideinches wide

LCM ProblemsLCM Problems
may be asking you:may be asking you:
 about an event that is orabout an event that is or
will be repeating over andwill be repeating over and
over.over.
 to purchase or get multipleto purchase or get multiple
items in order to haveitems in order to have
enough.enough.
 to figure out whento figure out when
something will happen atsomething will happen at
the same time.the same time.

LCM ExampleLCM Example
 Ben exercises every 12 daysBen exercises every 12 days
and Isabel every 8 days.and Isabel every 8 days.
Ben and Isabel bothBen and Isabel both
exercised today. How manyexercised today. How many
days will it be until theydays will it be until they
exercise together again?exercise together again?

Ben exercises every 12 days andBen exercises every 12 days and
Isabel every 8 days. Ben and IsabelIsabel every 8 days. Ben and Isabel
both exercised today. How manyboth exercised today. How many
days will it be until they exercisedays will it be until they exercise
together again?together again?
Ben exercises every 12 daysBen exercises every 12 days
and Isabel every 8 days andand Isabel every 8 days and
they both exercised today.they both exercised today.
 What do I need to know?What do I need to know?
How many days is it until theyHow many days is it until they
will both exercise on thewill both exercise on the
same day again.same day again.

This problem can be solved usingThis problem can be solved using
Least Common MultipleLeast Common Multiple becausebecause
we are trying to figure out whenwe are trying to figure out when
the soonestthe soonest (Least)(Least) time will betime will be
that as the event of exercisingthat as the event of exercising
continuescontinues (Multiple),(Multiple), it will occurit will occur
at the same timeat the same time (Common).(Common).
 I will find the LCM of 8 and 12.I will find the LCM of 8 and 12.
Ben exercises every 12 days andBen exercises every 12 days and
Isabel every 8 days. Ben andIsabel every 8 days. Ben and
Isabel both exercised today. HowIsabel both exercised today. How
many days will it be until theymany days will it be until they
exercise together again?exercise together again?

LCM Word Problem SolutionLCM Word Problem Solution
LCM using ‘List Method”LCM using ‘List Method”
88: 8, 16,: 8, 16, 2424, 32, 40, 32, 40
1212: 12,: 12, 2424,,
LCM using “Prime Factorization Method”LCM using “Prime Factorization Method”
8 =8 = 22 xx 22 x 2x 2
12 =12 = 22 xx 22 x 3x 3
(only use the common factors once)(only use the common factors once)
LCM =LCM = 22 xx 22 x 2 x 3 =x 2 x 3 = 2424
They will exercise together again inThey will exercise together again in 2424 days.days.

GCF AND LCMGCF AND LCM
 splitsplit
 to equallyto equally
distribute INTOdistribute INTO
largestlargest
 how many?how many?
 arrange somethingarrange something
into rows orinto rows or
groups.groups.
 event that is or willevent that is or will
be repeating.be repeating.
 get multiple itemsget multiple items
in order to havein order to have
enough.enough.
 to figure out whento figure out when
something willsomething will
happen at thehappen at the
same time.same time.

QUIZ!!!!!!QUIZ!!!!!!
 On a sheet of notebook paper, tellOn a sheet of notebook paper, tell
whether the following word problemswhether the following word problems
could be solved using GCF or LCM…could be solved using GCF or LCM…

Question #1Question #1
 Mrs. Evans has 120 crayons andMrs. Evans has 120 crayons and
30 pieces of paper to give to her30 pieces of paper to give to her
students. What is the largest # ofstudents. What is the largest # of
students she can have in her classstudents she can have in her class
so that each student gets equal #so that each student gets equal #
of crayons and equal # of paper.of crayons and equal # of paper.

 Rosa is making a game board that isRosa is making a game board that is
16 inches by 24 inches. She wants16 inches by 24 inches. She wants
to use square tiles. What is theto use square tiles. What is the
larges tile she can use?larges tile she can use?

 Z100 gave away a Z $100 bill forZ100 gave away a Z $100 bill for
every 100th caller. Every 30th callerevery 100th caller. Every 30th caller
received free concert tickets. Howreceived free concert tickets. How
many callers must get throughmany callers must get through
before one of them receivesbefore one of them receives bothboth aa
coupon and a concert ticket?coupon and a concert ticket?

 Two bikers are riding a circular path.Two bikers are riding a circular path.
The first rider completes a round inThe first rider completes a round in
12 minutes. The second rider12 minutes. The second rider
completes a round in 18 minutes. Ifcompletes a round in 18 minutes. If
they both started at the same placethey both started at the same place
and time and go in the sameand time and go in the same
direction, after how many minutesdirection, after how many minutes
will they meet again at the startingwill they meet again at the starting
point?point?

 Sean has 8-inch pieces of toy trainSean has 8-inch pieces of toy train
track and Ruth has 18-inch pieces oftrack and Ruth has 18-inch pieces of
train track. How many of each piecetrain track. How many of each piece
would each child need to build trackswould each child need to build tracks
that are equal in length?that are equal in length?

 I am planting 50 apple trees and 30I am planting 50 apple trees and 30
peach trees in rows. I want to mixpeach trees in rows. I want to mix
the apple and peach trees in mythe apple and peach trees in my
rows, and I want each row to be therows, and I want each row to be the
same. What is the maximum numbersame. What is the maximum number
of trees I can plant per row?of trees I can plant per row?

QUIZ Answers…QUIZ Answers…
 1.) GCF1.) GCF
 2.) GCF2.) GCF
 3.) LCM3.) LCM
 4.) LCM4.) LCM
 5.) LCM5.) LCM
 6.) GCF6.) GCF

QUIZ!!!!!!QUIZ!!!!!!
 Now…for some further practice, tryNow…for some further practice, try
to solve each of the 6 real-lifeto solve each of the 6 real-life
application problems. Be sure toapplication problems. Be sure to
give a sentence form answer thatgive a sentence form answer that
incorporates your LCM or GCFincorporates your LCM or GCF
solution.solution.
 Here are the real-life situations onceHere are the real-life situations once
again:again:

Question #1 ANSWERQuestion #1 ANSWER
 Mrs. Evans has 120 crayons and 30Mrs. Evans has 120 crayons and 30
pieces of paper to give to her students.pieces of paper to give to her students.
What is the largest # of students sheWhat is the largest # of students she
can have in her class so that eachcan have in her class so that each
student gets equal # of crayons andstudent gets equal # of crayons and
equal # of paper.equal # of paper.
 Answer: GCF= 30Answer: GCF= 30
Mrs. Evans could have 30 children in herMrs. Evans could have 30 children in her
class, each of whom will receive 1 piececlass, each of whom will receive 1 piece
of paper and 4 crayons.of paper and 4 crayons.

 Rosa is making a game board that is 16Rosa is making a game board that is 16
inches by 24 inches. She wants to useinches by 24 inches. She wants to use
square tiles. What is the larges tile shesquare tiles. What is the larges tile she
can use?can use?
 GCF = 8GCF = 8
The largest tile Rosa can use is 8 inches byThe largest tile Rosa can use is 8 inches by
8 inches. She will have a total of six 8”8 inches. She will have a total of six 8”
square tiles on her game board.square tiles on her game board.

 Z100 gave away a Z $100 bill for everyZ100 gave away a Z $100 bill for every
100th caller. Every 30th caller received100th caller. Every 30th caller received
free concert tickets. How many callersfree concert tickets. How many callers
must get through before one of themmust get through before one of them
receivesreceives bothboth a coupon and a concerta coupon and a concert
ticket?ticket?
 Answer: LCM = 300Answer: LCM = 300
The 300The 300thth
caller will be the first to receivecaller will be the first to receive
both a Z $100 bill and a concert ticket.both a Z $100 bill and a concert ticket.

 Two bikers are riding a circular path. TheTwo bikers are riding a circular path. The
first rider completes a round in 12first rider completes a round in 12
minutes. The second rider completes aminutes. The second rider completes a
round in 18 minutes. If they both startedround in 18 minutes. If they both started
at the same place and time and go in theat the same place and time and go in the
same direction, after how many minutessame direction, after how many minutes
will they meet again at the starting point?will they meet again at the starting point?
 ANSWER: LCM = 36ANSWER: LCM = 36
The two bikers will meet at the startingThe two bikers will meet at the starting
point again in 36 minutes.point again in 36 minutes.

 Sean has 8-inch pieces of toy train trackSean has 8-inch pieces of toy train track
and Ruth has 18-inch pieces of train track.and Ruth has 18-inch pieces of train track.
How many of each piece would each childHow many of each piece would each child
need to build tracks that are equal inneed to build tracks that are equal in
length?length?
 ANSWER: LCM = 72ANSWER: LCM = 72
Sean will need 9 of his 8” track pieces andSean will need 9 of his 8” track pieces and
Ruth will need 4 of her 18” track pieces inRuth will need 4 of her 18” track pieces in
order to build tracks of equal length. Theorder to build tracks of equal length. The
length of the tracks will be 72”.length of the tracks will be 72”.

Question #6Question #6 ANSWERANSWER
 I am planting 50 apple trees and 30 peachI am planting 50 apple trees and 30 peach
trees in rows. I want to mix the apple andtrees in rows. I want to mix the apple and
peach trees in my rows, and I want eachpeach trees in my rows, and I want each
row to be the same. What is the maximumrow to be the same. What is the maximum
number of trees I can plant per row?number of trees I can plant per row?
 ANSWER: GCF = 10ANSWER: GCF = 10
I will have 10 rows and each row will have 5I will have 10 rows and each row will have 5
apple trees and 3 peach trees.apple trees and 3 peach trees.

GREAT JOB!GREAT JOB!
You are learningYou are learning
to be quite theto be quite the
Problem Solver!Problem Solver!

Gcf and lcm (1)

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