Real Life Applications of GCF and LCM

Real Life Applications ofReal Life Applications ofGCF and LCMGCF and LCM

How can you tell if a word problem requires you How can you tell if a word problem requires you to use to use

Greatest Common Factor Greatest Common Factor or Least Common Multiple or Least Common Multiple

to solve?to solve?

GCF and LCMGCF and LCMProblem SolvingProblem Solving

First, use ourFirst, use our

PROBLEM SOLVING PROCESSPROBLEM SOLVING PROCESS

What do I know?What do I know? What do I need to What do I need to

know?know? What is my plan?What is my plan?

GCF Problems GCF Problems may be asking you:may be asking you:

to split things into smaller to split things into smaller sections?sections?

to equally distribute 2 or to equally distribute 2 or more sets of items into their more sets of items into their largest grouping?largest grouping?

to figure out how many to figure out how many people we can invite?people we can invite?

to arrange something into to 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 the One piece is 72 inches wide and the other piece is 90 inches wide. She other piece is 90 inches wide. She wants to cut both pieces into strips of wants to cut both pieces into strips of equal width that are as wide as equal width that are as wide as possible. How wide should she cut possible. How wide should she cut the strips?the strips?

Samantha has two pieces of cloth. One Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 72 inches wide and the other piece is 90 inches wide. She wants to piece is 90 inches wide. She wants to

cut both pieces into strips of equal cut both pieces into strips of equal width that are as wide as possible. How width that are as wide as possible. How

wide should she cut the strips?wide should she cut the strips?

What do I know?What do I know?

The pieces of cloth are 72 and 90 The 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 strips How wide should she cut the strips so that they are the largest so that they are the largest possible equal widths. possible equal widths.

What is my plan?What is my plan?This problem can be solved using This problem can be solved using

Greatest Common FactorGreatest Common Factor because we are cutting or because we are cutting or “dividing” the strips of cloth into “dividing” the strips of cloth into smaller pieces smaller pieces ((FactorFactor)) of 72 and of 72 and 90 90 ((CommonCommon)) and we are looking and we are looking for the widest possible strips for the 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. One Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 72 inches wide and the other piece is 90 inches wide. She wants to piece is 90 inches wide. She wants to

cut both pieces into strips of equal cut both pieces into strips of equal width that are as wide as possible. How width 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 SolutionGCF using ‘List Method”GCF using ‘List Method”

8 x 98 x 9 9 x 109 x 106 x 126 x 12 6 x 156 x 154 x4 x 1818 5 x 5 x 18183 x 243 x 24 3 x 303 x 302 x 362 x 36 2 x 452 x 451 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 x x 2 x 2 x 33 x x 3390 = 90 = 22 x x 33 x x 33 x 5 x 5

GCF = 2 x 3 x 3 = 18GCF = 2 x 3 x 3 = 18Samantha should cut each piece to be 18 Samantha should cut each piece to be 18

inches wideinches wide

LCM Problems LCM Problems may be asking you:may be asking you:

about an event that is or will about an event that is or will be repeating over and over.be repeating over and over.

to purchase or get multiple to purchase or get multiple items in order to have items in order to have enough.enough.

to figure out when to figure out when something will happen again something will happen again at the same time.at the same time.

LCM ExampleLCM Example

Ben exercises every 12 days Ben exercises every 12 days and Isabel every 8 days. and Isabel every 8 days. Ben and Isabel both Ben and Isabel both exercised today. How many exercised today. How many days will it be until they days will it be until they exercise together again?exercise together again?

Ben exercises every 12 days and Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel Isabel every 8 days. Ben and Isabel

both exercised today. How many both exercised today. How many days will it be until they exercise days will it be until they exercise

together again? together again? What do I know?What do I know? Ben exercises every 12 days Ben exercises every 12 days

and Isabel every 8 days and and 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 they How many days is it until they

will both exercise on the will both exercise on the same day again. same day again.

What is my plan?What is my plan?

This problem can be solved using This problem can be solved using Least Common MultipleLeast Common Multiple because because we are trying to figure out when the we are trying to figure out when the soonest soonest (Least)(Least) time will be that as time will be that as the event of exercising continues the event of exercising continues (Multiple),(Multiple), it will occur at the same it will occur at the same time 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 and Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel every 8 days. Ben and

Isabel both exercised today. How Isabel both exercised today. How many days will it be until they many days will it be until they

exercise together again? exercise together again?

LCM Word Problem SolutionLCM Word Problem SolutionLCM using ‘List Method”LCM using ‘List Method”

88: 8, 16, : 8, 16, 2424, 32, 40, 32, 401212: 12, : 12, 2424, ,

LCM using “Prime Factorization Method”LCM using “Prime Factorization Method”

8 = 8 = 22 x x 22 x 2 x 2 12 = 12 = 22 x x 22 x 3 x 3

(only use the common factors once)(only use the common factors once)LCM = LCM = 22 x x 22 x 2 x 3 = x 2 x 3 = 2424

They will exercise together again in They will exercise together again in 2424 days. days.

QUIZ!!!!!!QUIZ!!!!!!

On a sheet of notebook paper, tell On a sheet of notebook paper, tell whether the following word problems whether 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 and Mrs. Evans has 120 crayons and 30 pieces of paper to give to her 30 pieces of paper to give to her students. What is the largest # of students. What is the largest # of students she can have in her class students 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 is Rosa is making a game board that is 16 inches by 24 inches. She wants 16 inches by 24 inches. She wants to use square tiles. What is the to use square tiles. What is the larges tile she can use?larges tile she can use?


Z100 gave away a Z $100 bill for Z100 gave away a Z $100 bill for every 100th caller. Every 30th caller every 100th caller. Every 30th caller received free concert tickets. How received free concert tickets. How many callers must get through many callers must get through before one of them receives before one of them receives bothboth a a 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 in The first rider completes a round in 12 minutes. The second rider 12 minutes. The second rider completes a round in 18 minutes. If completes a round in 18 minutes. If they both started at the same place they both started at the same place and time and go in the same and time and go in the same direction, after how many minutes direction, after how many minutes will they meet again at the starting will they meet again at the starting point?point?


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


I am planting 50 apple trees and 30 I am planting 50 apple trees and 30 peach trees in rows. I want to mix peach trees in rows. I want to mix the apple and peach trees in my the apple and peach trees in my rows, and I want each row to be the rows, and I want each row to be the same. What is the maximum number same. 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, try Now…for some further practice, try to solve each of the 6 real-life to solve each of the 6 real-life application problems. Be sure to application problems. Be sure to give a sentence form answer that give a sentence form answer that incorporates your LCM or GCF incorporates your LCM or GCF solution. solution.

Here are the real-life situations once Here are the real-life situations once again:again:


Mrs. Evans has 120 crayons and Mrs. Evans has 120 crayons and 30 pieces of paper to give to her 30 pieces of paper to give to her students. What is the largest # of students. What is the largest # of students she can have in her class students 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.

Question #1 ANSWERQuestion #1 ANSWER Mrs. Evans has 120 crayons and 30 Mrs. 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 she What is the largest # of students she can have in her class so that each can have in her class so that each student gets equal # of crayons and student gets equal # of crayons and equal # of paper.equal # of paper.

Answer: GCF= 30Answer: GCF= 30Mrs. Evans could have 30 children in her Mrs. Evans could have 30 children in her

class, each of whom will receive 1 piece class, 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 Rosa is making a game board that is 16 inches by 24 inches. She wants 16 inches by 24 inches. She wants to use square tiles. What is the to use square tiles. What is the larges tile she can use?larges tile she can use?

Question #2 ANSWERQuestion #2 ANSWER

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

GCF = 8GCF = 8

The largest tile Rosa can use is 8 inches by 8 The largest tile Rosa can use is 8 inches by 8 inches. She will have a total of six 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 Z100 gave away a Z $100 bill for every 100th caller. Every 30th caller every 100th caller. Every 30th caller received free concert tickets. How received free concert tickets. How many callers must get through many callers must get through before one of them receives before one of them receives bothboth a a coupon and a concert ticket?coupon and a concert ticket?

Question #3 ANSWERQuestion #3 ANSWER

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

Answer: LCM = 300Answer: LCM = 300The 300The 300thth caller will be the first to receive caller 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. Two bikers are riding a circular path. The first rider completes a round in The first rider completes a round in 12 minutes. The second rider 12 minutes. The second rider completes a round in 18 minutes. If completes a round in 18 minutes. If they both started at the same place they both started at the same place and time and go in the same and time and go in the same direction, after how many minutes direction, after how many minutes will they meet again at the starting will they meet again at the starting point?point?

Question #4 ANSWERQuestion #4 ANSWER Two bikers are riding a circular path. The Two bikers are riding a circular path. The

first rider completes a round in 12 first rider completes a round in 12 minutes. The second rider completes a minutes. The second rider completes a round in 18 minutes. If they both started round in 18 minutes. If they both started at the same place and time and go in the at the same place and time and go in the same direction, after how many minutes same 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 = 36The two bikers will meet at the starting point The two bikers will meet at the starting point

again in 36 minutes.again in 36 minutes.


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

Question #5 ANSWERQuestion #5 ANSWER Sean has 8-inch pieces of toy train track Sean 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 child How many of each piece would each child need to build tracks that are equal in need to build tracks that are equal in length?length?

ANSWER: LCM = 72ANSWER: LCM = 72Sean will need 9 of his 8” track pieces and Sean will need 9 of his 8” track pieces and

Ruth will need 4 of her 18” track pieces in Ruth will need 4 of her 18” track pieces in order to build tracks of equal length. The order to build tracks of equal length. The length of the tracks will be 72”.length of the tracks will be 72”.


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

Question #6Question #6 ANSWERANSWER

I am planting 50 apple trees and 30 peach I am planting 50 apple trees and 30 peach trees in rows. I want to mix the apple and trees in rows. I want to mix the apple and peach trees in my rows, and I want each peach trees in my rows, and I want each row to be the same. What is the maximum row 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 5 I 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 learning to be quite the You are learning to be quite the

Problem Solver!Problem Solver!

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Real Life Applications of GCF and LCM