LEAST COMMON MULTIPLE STANDARD:

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Presentation transcript:

LEAST COMMON MULTIPLE STANDARD: M6N1.c. Determine the least common multiple (LCM) for a set of numbers.

What is a Multiple? A multiple of a number is the product of the number and any nonzero whole number. Example: 2 x 3 = 6 2 x 4 = 8 2 x 5 = 10 6, 8, and 10 are multiples of 2

What is a Common Multiple? A multiple that is shared by two or more numbers is called a Common Multiple Example: Multiples of 4: 4, 8,12, 16, 20, 24, 28,32,36 Multiples of 6: 6, 12, 18, 24, 30,36 12, 24, and 36 are Common Multiples of 4 and 6

What is a Least Common Multiple? The smallest or least of the common multiples is the Least Common Multiple (LCM). Example: Multiples of 4: 4, 8,12,16,20,24,28,32,36 Multiples of 6: 6,12,18,24,30,36 12, 24, and 36 are Common Multiples of 4 and 6 But 12 is the Least Common Multiple

Let’s Do Another One Find the Least Common Multiple of 4 and 8 Multiples of 8: 8,16,24,32,40,48,56,64 Multiples of 10: 10, 20, 30, 40, 50, 60, The Least Common Multiple is: 40 Put another way, 40 is the smallest multiple that 8 and 10 have in common

LCM story problems Let’s say you are having a hot dog party. Hot Dogs come in packs of 10 and Hot Dog buns come in packs of 8. What is the least number of packs you can buy and have none left over? The answer is the LCM!

Find the LCM Using the Ladder Method Buns Hot Dogs 2 8 10 4 5 LCM: 2 x 4 x 5 = 40

It’s a Party! the LCM of 8 and 10 is 40. So you need to buy 4 packs of Hot Dogs (4 x 10 = 40) and 5 packs of Hot Dog Buns (8 x 5 = 40).

See a movie, Get a Prize! A movie theater gives a free soda to every 40th customer and a free popcorn to every 24th customer. Which customer will be the first to win both a FREE soda and a free popcorn?

Find the LCM Using the Ladder Method Soda Popcorn 4 40 24 2 10 6 5 3 LCM: 4 x 2 x 5 x 3 = 120 Every 120th person will receive both a soda and popcorn

How to Recognize an LCM Story Problem Look for these key words: Least Smallest First Look for these concepts: Buying or selling things in packs or multiples Finding something that happens first Finding something that happens again and again (trains, bikes, cars on a circular track, Ferris wheels, gears)

Now It’s Your Turn Work in groups of 4 Work together to solve your story problem Choose a member from your group to go to the board and explain how you solved your problem