least common multiple least common denominator by monica yuskaitis editied by ladora loggins

Least Common Least Common Multiple Least Multiple Least

Common DenominatorCommon DenominatorBy Monica Yuskaitis By Monica Yuskaitis

Editied by LaDora LogginsEditied by LaDora Loggins

ProductProduct

The answer to a The answer to a multiplication problem.multiplication problem.

6 X 6 = 36

What is the product?What is the product?

7 X 8 = 56

What is the product?What is the product?

8 X 9 = 72

MultipleMultiple

The product of two whole The product of two whole numbers multiplied togethernumbers multiplied together

Some multiples of 6 1∙6=6, 2∙6=12, 3∙6=18,

4∙6=24, 5∙6=30, 6∙6=36, 7∙6=42, 8∙6=48, 9∙6=54…

Without actually multiplying, Without actually multiplying, Name some multiples of 5Name some multiples of 5

5, 10, 15, 20, 25, 30, 35

So… we can see that multiples are the So… we can see that multiples are the same as counting up by a certain factor.same as counting up by a certain factor.

Without actually Without actually multiplying, Name some multiplying, Name some

multiples of 7multiples of 7

7, 14, 21, 28, 35, 42, 49So… by what factor were we counting up?

7

Name some multiples of Name some multiples of 44

4, 8, 12, 16, 20, 24, 28

Name some multiples of Name some multiples of 99

9, 18, 27, 36, 45, 54, 63

A Common MultipleA Common Multiple

A number that is a multiple A number that is a multiple of two or more numbers.of two or more numbers.

Lets look at 3 and 6

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42…

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60…

Which multiples do they have in common?

6, 12, 18, 24, 30, 36, 42, 48

What are some Common What are some Common Multiples for 2 & 8?Multiples for 2 & 8?

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34…

8: 8, 16, 24, 32, 40, 48, 56…

What are some of the multiples they have in common? 8, 16, 24, 32, ….

What are some Common What are some Common Multiples for 4 & 6?Multiples for 4 & 6?

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60…

What are some of the multiples they have in common? 12, 24, 36, 48….

What are 3 Common What are 3 Common Multiples for 3 & 7?Multiples for 3 & 7?

21, 42, 63

What are 6 Common What are 6 Common Multiples for 5 & 10?Multiples for 5 & 10?

10, 20, 30, 40, 50, 60

A Least Common A Least Common MultipleMultiple

The smallest common The smallest common multiple of a set of two or multiple of a set of two or more numbers.more numbers.

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

5 = 5, 10, 15, 20, 25, 30

What is the Least What is the Least Common Multiple of 3 & Common Multiple of 3 &

88

8 = 8, 16, 24, 32, 40, 48 3 = 3, 6, 9, 12, 15, 21, 24

Or we can use the “L” Method

We can list them out

3 81

3 8

Take out the GCF and thenMultiply all the numbers in the “L” 24

What is the Least What is the Least Common Multiple of 4 & Common Multiple of 4 &

88

8 = 8, 16, 24, 32, 40, 48 4 = 4, 8, 12, 16, 20, 24

4 82

2 4 2

1 2 8

Take out the GCF and thenMultiply all the numbers in the “L”

What is the Least What is the Least Common Multiple of 6 & Common Multiple of 6 &

88

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

6 82

3 4 24

Take out the GCF and thenMultiply all the numbers in the “L”

What is the Least What is the Least Common Multiple of 4 & Common Multiple of 4 &

1010

10 = 10, 20, 30, 40, 50, 4 = 4, 8, 12, 16, 20, 24

4 102

2 5

Take out the GCF and thenMultiply all the numbers in the “L” 20

What is the Least What is the Least Common Multiple of 3 & Common Multiple of 3 &

99

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

Multiply all the numbers in the “L” 3 93

1 3 9

To Add or Subtract To Add or Subtract Fractions With Unlike Fractions With Unlike

DenominatorsDenominators Remember! Yesterday we learned that to add or Remember! Yesterday we learned that to add or

subtract fractions they needed to have the same subtract fractions they needed to have the same denominator. denominator.

1= 5, 10, 15, 20, 25, 30

1= 10, 20, 30, 40, 50+

5

10

If they do not, then we can not operate until they If they do not, then we can not operate until they do.do.

To Add or Subtract To Add or Subtract Fractions With Unlike Fractions With Unlike

DenominatorsDenominators Compare the lists of multiples. Compare the lists of multiples.

Circle the common multiples Circle the common multiples between the two lists.between the two lists.

15 = 5, 10, 15, 20, 25, 301

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

To Add or Subtract To Add or Subtract Fractions With Unlike Fractions With Unlike

DenominatorsDenominators

Use the lowest common Use the lowest common multiple as the denominator.multiple as the denominator.

15 = 5, 10, 15 ,20 ,25 ,301

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

To Add or Subtract To Add or Subtract Fractions With Unlike Fractions With Unlike

DenominatorsDenominators

This number is also called the This number is also called the least common denominator.least common denominator.

15 = 5, 10, 15 ,20 ,25 ,301

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

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

12 = 2, 4, 6, 8, 10, 1218 = 8, 16, 24, 32, 40+

2 82

1 4 8

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

110 = 10, 20, 30, 40, 18 = 8, 16, 24, 32, 40+

8 102

4 540

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

110 = 10, 20, 30, 40, 14 = 4, 8, 12, 16, 20, +

10 42

5 220

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

12 = 2, 4, 6, 8, 10, 14 = 4, 8, 12, 16, 20, +

42 42

1 2

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

12 = 2, 4, 6, 8, 10, 12 112 = 12, 24, 36, 48 +

2 122

1 612

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

13 = 3, 6, 9, 12, 15 14 = 4, 8, 12, 16, 20, +

3 41

3 412

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

13 = 3, 6, 9, 12, 15 15 = 5, 10, 15, 20, 25, +

153 51

3 5

Find the Least Common Find the Least Common Denominator or Least Common Denominator or Least Common

MultipleMultiple

13 = 3, 6, 9, 12, 15 19 = 9, 18, 27, 36, 45, +

93 93

1 3