Transcript Lesson 3.4
Lesson 3.4 Core Focus on Decimals & Fractions Least Common Multiple Warm-Up 1. Find the value of 7 × 1. 7 2. Find the value of 7 × 2. 14 3. Find the value of 7 × 3. 21 4. Find the value of 7 × 4. 28 5. What is the prime factorization of 32? 22222 Lesson 3.4 Least Common Multiple Find the least common multiple for a set of numbers. Find the least common denominator for a set of fractions. Vocabulary Multiple The product of a given number and a whole number Least Common Multiple (LCM) The smallest multiple (not zero) that is common to two or more numbers. Least Common Denominator (LCD) Least common multiple of two or more denominators. In the model above, the multiples of 4 are in blue squares and the multiples of 5 are circled in red. Twenty is a common multiple of 4 and 5. Least Common Multiple (LCM) List the multiples of the given numbers until you find the first multiple that is common to all given numbers. - OR Use prime factorization of the given numbers to identify prime factors. Identify the common prime factors. Find the product of the common prime factors and any remaining factors. Example 1 List the first five positive multiples of 3 and 6. Find the LCM. Write the multiples of 3 and 6. The first number to appear in both lists is 6. List the multiples for each number. The least common multiple (LCM) is 6. 3: 3, 6, 9, 12, 15… 6: 6, 12, 18, 24, 30… Example 2 Courtney and Kaysha are cousins. Courtney visits her grandparents every 30 days. Kaysha visits her grandparents every 20 days. They both visited their grandparents today. How long will it be before they are together at their grandparents’ house on the same day? List the multiples of each number. 20: 20, 40, 60, 80, 100, 120, 140, 160, 180… 30: 30, 60, 90, 120, 150, 180… Find the common multiples. Common multiples of 20 and 30 are: 60, 120, 180 Identify the LCM. LCM = 60 Courtney and Kaysha will be at their grandparents’ house together in 60 days. Example 3 Sean and Deion both rented movies today. Sean rents a movie every 10 days. Deion rents a movie every 15 days. How many days until they rent movies on the same day again? Write the prime factorization for each number. Identify the common prime factors (circled). Find the LCM by finding the product of the common prime factors one time and any remaining prime factors. LCM = 2 3 5 = 30 Sean and Deion will rent movies on the same day again in 30 days. Example 4 Ling, Kara and Sasha saw each other at the ice skating rink today. Ling goes to the rink every 2 days. Kara goes to the rink every 4 days. Sasha goes to the rink every 6 days. How many days until they are together at the rink again? List multiples of each number. 2: 2, 4, 6, 8, 10, 12, … 4: 4, 8, 12, 16, 20, 24, … 6: 6, 12, 18, 24, 30, 36, … Identify the LCM. LCM = 12 Ling, Kara and Sasha will be at the rink together in 12 days. Example 5 3 1 and . Find the least common denominator of 8 2 Identify the denominators. 8 and 2 List the multiples of both denominators. 8: 8, 16, 24, 32, 40, … 2: 2, 4, 6, 8, 10, 12, … The least common denominator is 8. The LCM is the LCD. Communication Prompt What is an example of a situation where it would be necessary to find the LCM of four or more numbers? Exit Problems 1. Find the LCM of 18 and 24. 72 2. Find the LCM of 10, 20 and 25. 100 1 5 and ? 3. What is the LCD of 12 18 36