Least Common Multiples and Least Common Denominator

Here are the first ten multiples of 3 and 5.

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Which multiple is the Least Common Multiple (LCM) of 3 and 5?

• The LCM is 10

• The LCM is 12

• The LCM is 15

• The LCM is 30

Answer explanation

15 and 20 are both common multiples of 3 and 5! But the LEAST common multiple is 15 because 15 is less than 20 and the first multiple that has the factors 3 and 5.

Tags

CCSS.6.NS.B.4

What is the Least Common Multiple (LCM) of 4 and 5?

(Hint! Make a list of multiples by counting by 4 and 5 and see what is the first multiple that is the same on both lists)

• The LCM is 20

• The LCM is 40

• The LCM is 25

• The LCM is 36

Answer explanation

The LCM of 4 and 5 is 20! It's the first multiple on both lists and has the factor 4 and 5.

Tags

CCSS.4.OA.B.4

What is the Least Common Multiple (LCM) of 2 and 4?

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

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

(Hint! Look for the first number that is the same on both lists!)

• The LCM is 4

• The LCM is 8

• The LCM is 12

• The LCM is 16

Answer explanation

The LCM of 2 and 4 is 4! It's the first multiple that is the same on both lists and has the factors 2 and 4!

Fun fact! All the multiples of 4 are common multiples of 2 because all the multiples of 4 are even numbers!

Tags

CCSS.6.NS.B.4

What is the LCM of 3 and 6?

(Hint! Make a list of multiples for 3 and 6 and see what is the first common multiple on both lists!)

• The LCM is 3

• The LCM is 6

• The LCM is 9

• The LCM is 12

Answer explanation

The LCM of 3 and 6 is 6!

Fun fact! All the multiples of 6 are also common multiples of 3!

Tags

CCSS.4.OA.B.4

What is the LCM of 10 and 12?

(Make a lists of multiples for 10 and 12 and look for the first multiple that is the same!)

• The LCM is 20

• The LCM is 40

• The LCM is 60

• The LCM is 80

Answer explanation

The LCM for 10 and 12 is 60!

Fun fact! If you are trying to find the least common multiple of a number and 10, look for the first multiple of the other number that ends with a zero!

Tags

CCSS.4.OA.B.4

Challenge!

What is the LCM of 12 and 20?

• The LCM is 20

• The LCM is 40

• The LCM is 60

• The LCM is 80

Answer explanation

The LCM of 12 and 20 is also 60!

Now it's time to use what you have learned about Least Common Multiple (LCM) to find the Least Common Denominator (LCD) of two fractions!

Are you ready to try it out? Pick the image for how you feel.

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What is the Least Common Denominator (LCD) of the fractions 1/2 and 1/4?

(Hint! Find the Least Common Multiple (LCM) of 2 and 4 )

• The LCD is 16

• The LCD is 12

• The LCD is 8

• The LCD is 4

Answer explanation

The least common multiple of 2 and 4 was 4!

So the least common denominator of 1/2 and 1/4 is also 4!

Tags

CCSS.4.NF.A.2

Since the LCD of 1/2 and 1/4 is 4, I can find an equivalent fraction for 1/2 that has 4 as a denominator.

What is the equivalent fraction of 1/2 that has 4 as a denominator?

(Hint! Multiply the numerator and denominator by the same factor so that the denominator becomes 4 )

• 3/4

• 2/4

• 4/4

• 1/4

Answer explanation

If you multiply the numerator and denominator of 1/2 by 2, you will get 2/4 which has 4 as the denominator.

1/2 is equivalent to 2/4.

Tags

CCSS.3.NF.A.3B

CCSS.4.NF.A.1

So now that you changed 1/2 to 2/4, you have the fraction 2/4 and 1/4 which both have a common denominator now!

Complete this sentence!

"They are fractions with common denominators because..."

• both 2/4 and 1/4 have 4 as the denominator.

• both 2/4 and 1/4 have even numbers.

• both 2/4 and 1/4 are equivalent.

• both 2/4 and 1/4 are fractions.

Tags

CCSS.3.NF.A.3A

CCSS.3.NF.A.3B

CCSS.4.NF.A.1