1 / 15

# Least Common Multiple (LCM) - PowerPoint PPT Presentation

Least Common Multiple (LCM). Vocabulary. Multiple The product of a number and any whole number Think of your multiplication chart… Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, etc. Common Multiple Multiples that numbers both have Common Multiples of 2 & 3: 6, 12, 18, 24, 30, 36, etc.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Least Common Multiple (LCM)' - lin

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Least Common Multiple (LCM)

• Multiple

• The product of a number and any whole number

• Think of your multiplication chart…

• Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, etc.

• Common Multiple

• Multiples that numbers both have

• Common Multiples of 2 & 3: 6, 12, 18, 24, 30, 36, etc.

• Least Common Multiple (LCM)

• The smallest multiple that numbers share

• LCM of 2 & 3: 6

• To find a common denominator before we add or subtract fractions.

1. Listing Multiples

2. Prime Factorization

3. Downward Division

• Find the LCM of the numbers: 5 & 10

• Multiples of 5:

• 5, 10, 15, 20, 25, 30, 35, 40…

• Multiples of 10:

• 10, 20, 30, 40, 50, 60, 70…

• Least Common Multiple: 10

• Benefits

• Easy strategy

• Missing multiples, wrong multiples

Listing Multiples

• Find the Prime Factorization

47

2 2

4: 22 7: 7

• Take all the bases that the numbers have and then the largest exponent for each base

2271

2271=28

• Benefits

• Ensures you have all the prime numbers

• Some find factor trees confusing

Prime Factorization

• Divide on the left by prime numbers that divide both numbers. Continue until you get prime numbers on the bottom of the tower.

2 6 16

3 8

• Combine the values on the left and the bottom row and evaluate for an answer

HINT: Make an “L” with the numbers to

multiply together

2 ● 3 ● 8 = 48

• Benefits

• Only have to divide by prime numbers, then multiply down the left side and the bottom.

• Some find downward division confusing.

Downward Division

• Find the LCM of the following pair of numbers:

• 3, 7

• 12, 18

• 5, 13

• 3, 5, 12

3. What is the LCM of 5, 13

5. Jośe is shopping for party supplies. He finds a package of 10 plates, a package of 16 napkins, and a package of 8 cups. What is the least number of packages of plates, napkins, and cups that Jośe can buy so that he has the same number of each?

Find the LCM of the 3 numbers.

• Choose any method (listing multiples, prime factorization, downward division)

• The LCM of 10, 16, and 8 is 80

• 10 x ___ = 80 8 packages of plates

• 16 x ___ = 80 5 packages of napkins

• 8 x ___ = 80 10 packages of cups