5-1 Least Common Multiple Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

5-1 Least Common Multiple Do Now Write the first five multiples of each number , 10, 15, 20, 25 6, 12, 18, 24, 30 10, 20, 30, 40, 50 12, 24, 36, 48, 60

5-1 Least Common Multiple SWBAT find the least common multiple (LCM) of a group of numbers using two methods. Objective

5-1 Least Common Multiple Vocabulary least common multiple (LCM) ‏

5-1 Least Common Multiple A multiple of a number is the product of the number and any nonzero whole number. Remember!

5-1 Least Common Multiple Ex. 1 Consumer Application English muffins come in packs of 8, and eggs come in cartons of 12. If there are 24 students, what is the least number of packs and cartons needed so that each student has a muffin sandwich with one egg and there are none left over? There are 24 English muffins and 24 eggs. So 3 packs of English muffins and 2 cartons of eggs are needed. Draw muffins in groups of 8. Draw eggs in groups of 12. Stop when you have drawn the same number of each.

5-1 Least Common Multiple Try this one on your own… There are 18 dog cookies and 18 bones. So 3 packages of dog cookies and 2 bags of bones are needed. Dog cookies come in packages of 6, and bones in bags of 9. If there are 18 dogs, what is the least number of packages and bags needed so that each dog has a treat box with one bone and one cookie and there are no bones or cookies left over? Draw cookies in groups of 6. Draw bones in groups of 9. Stop when you have drawn the same number of each.

5-1 Least Common Multiple Try this one on your own… Hotdogs come in packages of 10, and buns come packages of 8. If you are throwing a BBQ party and want to serve hotdogs with buns, what is the least amount of hotdogs and buns you would have to buy so that there are no remaining hotdogs and buns?

5-1 Least Common Multiple The smallest number that is a multiple of two or more numbers is the least common multiple (LCM). In Additional Example 1, the LCM of 8 and 12 is 24.

5-1 Least Common Multiple Ex. 2 - Using Multiples to Find the LCM Find the least common multiple (LCM). Method 1: Use a list. 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44,... 5, 10, 15, 20, 25, 30, 35, 40, 45,... 8, 16, 24, 32, 40, 48,... LCM: 40 List multiples of 4, 5, and 8. Find the smallest number that is in all the lists. 4, 5, and 8 4: 5: 8:

5-1 Least Common Multiple The prime factorization of a number is the number written as a product of its prime factors. Remember!

5-1 Least Common Multiple Ex. 3 - Using Multiples to Find the LCM Find the least common multiple (LCM). Method 2: Use prime factorization. 6 and 20

1-2 Divide Multi-Digit Whole Numbers 1.) What is the prime factorization of each number? 2.) Did I line up the factors from least to greatest? 3.) Did I use the exponent from each factor? 4.) Did I multiply?

1-2 Divide Multi-Digit Whole Numbers Ex. 3 - Using Multiples to Find the LCM Find the least common multiple (LCM). Method 2: Use prime factorization. 6 and 20 1.) What is the prime factorization of each number? 2.) Did I line up the factors from least to greatest? 3.) Did I exponent from each factor? 4.) Did I multiply?

5-1 Least Common Multiple Ex. 4 Find the least common multiple (LCM). 15, 6, and 4 1.) What is the prime factorization of each number? 2.) Did I line up the factors from least to greatest? 3.) Did I exponent from each factor? 4.) Did I multiply?

5-1 Least Common Multiple Try this one on your own… ( Use a list) Find the least common multiple (LCM). 3, 4, and 9

5-1 Least Common Multiple Try this one on your own… ( Use prime factorization) Find the least common multiple (LCM). 4 and 10

5-1 Least Common Multiple Try this one on your own… (Use any method you desire) Find the least common multiple (LCM). 12, 6, and 8

5-1 Least Common Multiple Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

5-1 Least Common Multiple Exit Ticket Find the least common multiple (LCM). 1. 6, , , 6, , 16, 24, Two students in Mrs. Albring’s preschool class are stacking blocks, one on top of the other. Reece’s blocks are 4 cm high, and Maddy’s blocks are 9 cm high. How tall will their stacks be when they are the same height for the first time? 36 cm

5-1 Least Common Multiple 1. Identify the least common multiple (LCM). 8, 18 A. 144C. 72 B. 120D. 64 Lesson Quiz for Student Response Systems

5-1 Least Common Multiple 2. Identify the least common multiple (LCM). 9, 24 A. 72C. 52 B. 64D. 27 Lesson Quiz for Student Response Systems

5-1 Least Common Multiple 3. Identify the least common multiple (LCM). 3, 15, 18 A. 94C. 54 B. 90D. 24 Lesson Quiz for Student Response Systems

5-1 Least Common Multiple 4. Identify the least common multiple (LCM). 9, 12, 18, 27 A. 108C. 172 B. 144D. 216 Lesson Quiz for Student Response Systems

5-1 Least Common Multiple 5. Water colors come in boxes of 6 and brushes come in packets of 10. Tom wants to give each of 30 students a water color and a brush. What is the least number of boxes and packs he should buy so there are none left over? A. 3 boxes of water colors and 5 packs of brushes B. 5 boxes of water colors and 3 packs of brushes C. 4 boxes of water colors and 2 packs of brushes D. 2 boxes of water colors and 4 packs of brushes Lesson Quiz for Student Response Systems