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Least Common Multiple (LCM)

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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Least Common Multiple (LCM)

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  1. Least Common Multiple (LCM)

  2. 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

  3. What would I use an LCM for? • To find a common denominator before we add or subtract fractions.

  4. How do I find the LCM of 2 numbers? 1. Listing Multiples 2. Prime Factorization 3. Downward Division

  5. 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

  6. 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

  7. 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

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

  9. 1. What is the LCM of 3, 7

  10. 2. What is the LCM of 12, 18

  11. 3. What is the LCM of 5, 13

  12. 4. What is the LCM of 3, 5, 12

  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?

  14. 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

  15. Please begin the problems on pages 208-209 in the red text books…# 11, 33-36

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