Copyright©amberpasillas2010 Least Common Multiple LCM 2 Methods

copyright©amberpasillas2010

Least Common Multiple

LCM

2 Methods


Product

The answer to a multiplication problem.

6 X 6 = 36


What is the product?

7 X 8 = 56


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 Multiple A 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



Smallestnumber that a set of given numbers dividesevenly 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 # 1TO 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



& 8

8 = 8, 16, 24, 32, 40, 48 6 = 6, 12, 18, 24, 30, 36



& 9

9 = 9, 18, 27, 36, 45, 54 3 = 3, 6, 9, 12, 15, 21,


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 2Then select the remaining factors.

3 3 2 5LCM 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 2LCM 360

72

8 9

3 32 4

2 2

2




48 80224 40212 2026 1023 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



The GCF and LCM are used so regularly thatmost people find them mentally.

GCF = 1

LCM = 72

GCF = 5

LCM = 60

1) 8 9 2) 15 20




The GCF and LCM are used so regularly thatmost people find them mentally.

GCF = 4

LCM = 60

GCF = 4

LCM = 24

1) 12 20 2) 8 12




THE ENDTake Out Your Study Guide!!!



#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.

202 10

2 5

2 2 5

182 9

3 3

2 3 3

2) Select all common factors once.

LCM 23) Select all remaining factors, and multiply.

3 3 2 5 LCM 180

#11 LCM Prime Factorization Method # 2

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Copyright©amberpasillas2010 Least Common Multiple LCM 2 Methods