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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.

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Vocabulary
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
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
How do I find the LCM of 2 numbers?

1. Listing Multiples

2. Prime Factorization

3. Downward Division


Listing multiples

  • 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

  • Disadvantages

    • Missing multiples, wrong multiples

Listing Multiples


Prime factorization

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

  • Evaluate for an answer

    2271=28

  • Benefits

    • Ensures you have all the prime numbers

  • Disadvantages

    • Some find factor trees confusing

Prime Factorization


Downward division

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.

  • Disadvantages

    • Some find downward division confusing.

Downward Division


Now try these
Now Try These…

  • 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
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?


5 answers
5. Answers…

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



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