Least Common Multiple (LCM)

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# 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 &amp; 3: 6, 12, 18, 24, 30, 36, etc.

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### 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.
• Least Common Multiple (LCM)
• The smallest multiple that numbers share
• LCM of 2 & 3: 6
What would I use an LCM for?
• To find a common denominator before we add or subtract fractions.
How do I find the LCM of 2 numbers?

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 LCM of the numbers: 4 & 7

• 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

Find the LCM of the numbers: 6 & 16

• 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
Now Try These…
• Find the LCM of the following pair of numbers:
• 3, 7
• 12, 18
• 5, 13
• 3, 5, 12

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