least common multiple - american baccalaureate schoolhandouts.abs.edu.kw/mshs/assignments...

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Least Common Multiple

LCM


Essential Question:How do I find the least common multiple

of two or three numbers, and why is this relevant to me?

Common Core Objective:6.NS.4

Common Core Objective:Students will be able to identify the least common

multiple of two or three one, two, and three digit numbers.

Least Common Multiple (LCM)


When thinking about finding the Least Common Multiple, or the LCM…

REMEMBER

L…The smallest number

C…all terms in common

M…from their list of multiples



Important to Remember…

There are THREE methods for finding the Common Multiples of two or

more numbers…

Method 1…Use Multiple ListsMethod 2…Use Prime FactorizationMethod 3…Multiply the Numbers***



Multiple

The product of a whole number

multiplied times any other whole

number.

Name the first six multiples of 6

6, 12, 18, 24, 30, 36


Name the first six

multiples of 5

5, 10, 15, 20, 25, 30


Common MultipleA Common Multiple is a number

that is a multiple of two numbers.

Here are common multiples for the

numbers 4 and 10

10 = 10, 20, 30, 40, 50,

4 = 4, 8, 12, 16, 20, 24



Smallest

number that a set of given numbers divides

evenly into.

LCM - Least Common Multiple -

It is useful to know how to do this so you

can find a common denominator when

adding or subtracting fractions.

THERE ARE TWO WAYS TO FIND LCM



Method # 1

TO FIND THE LCM OF TWO NUMBERS

• Find the least multiple that

both numbers have in common.

•List the multiples of both numbers


Least Common Multiple Method # 1

Make a List of Multiples

Find the LCM of 10 and 12.

10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

12: 12, 24, 36, 48, 60

LCM = 60

...



Make a List of Multiples


32: 32 , 64, 96, 128, 160, 192, 224, 256

40: 40, 80, 120, 160

LCM = 160

...


What is the Least Common

Multiple of 4 & 10

10 = 10, 20, 30, 40, 50,

4 = 4, 8, 12, 16, 20, 24



Multiple of 6 & 8

8 = 8, 16, 24, 32, 40, 48

6 = 6, 12, 18, 24, 30, 36



Multiple of 3 & 9

9 = 9, 18, 27, 36, 45, 54

3 = 3, 6, 9, 12, 15, 21,


Guided Practice ProblemsDirections: Find the LCM for each number set.

1. 9 and 12

2. 4, 8, and 12

3. 2, 3, 6, and 8



Independent Practice ProblemsDirections: Find the LCM for each number set.

1. 6 and 10

2. 2, 4, and 5

3. 4, 6, and 8



Method #1 is easy to do!

Method #1 is a good method if both of your

numbers are really small.

What if you have really large numbers? It

might take too long to keep listing

multiples until you find a common

multiple.SO HERE IS METHOD # 2


1) Write the prime factorization of

each number.

3) Then select the remaining factors

and multiply.

2) Select all common factors ONCE.



20

2 10

2 5

2 2 5

18

2 9

3 3

2 3 3

Select all common factors once.

LCM 2

Then select the remaining factors.

3 3 2 5

LCM 180



2 2 2 3 3

45

5 9

3 3

3 3 5

Select all common factors once.

LCM 3Then select the remaining factors.

3 5 2 2

LCM 360

72

8 9

3 32 4

2 2

2




48 802

24 402

12 202

6 102

3 5

Common FactorsOnce

Remaining Factors

LCM

LCM 240

2 3222 5



SO I GUESS YOU ARE WONDERING

When Are We Ever Gonna

Have To Use This?



What is the LCM used for?The LCM is used to find common denominatorsso that fractions may be easily compared, added,or subtracted.

5

8

7

12

8 1224 622 3

LCM 2 2 2 3

LCM 24

24 24

15 14

33 2

2



#9 MultiplesA number that is added to itself

becomes a multiple.

Multiples of 3 = 3, 6, 9, 12, 15, 18 . . .

Multiples can go on infinitely forever.

It is useful to know this for adding fractions.

The least common multiple (LCM) is the

least common number that is a multiple of 2

numbers.


LCM Make a List Method # 1

TO FIND THE LCM OF 4 and 12:

2) Find the least multiple that both numbers have in common.

1) List the multiples of both numbers

4 = 4, 8, 12, 16, 20…

12 = 12, 24, 36…

LCM is 12

#10

This method is useful if both numbers are small.


1) List the prime factorization to find the LCM.

20

2 10

2 5

2 2 5

18

2 9

3 3

2 3 3

2) Select all common factors once.

LCM 2

3) Select all remaining factors, and multiply.

3 3 2 5 LCM 180

#11 LCM Prime Factorization Method # 2

least common multiple - american baccalaureate schoolhandouts.abs.edu.kw/mshs/assignments...

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