2-6 Least Common Multiple Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up Write the prime factorization of each number Find the greatest common factor and and and · · · 5 · 47 Course Least Common Multiple

Problem of the Day Franklin had some counters. When he counted them by twos, threes, fours, and fives, he had one left over. If Franklin had more than 100 and fewer than 150 counters how many did he have? 121 Course Least Common Multiple

Learn to find the least common multiple of two or more whole numbers. Course Least Common Multiple

Vocabulary multiple least common multiple (LCM) Insert Lesson Title Here Course Least Common Multiple

Course Least Common Multiple The maintenance schedule on Ken’s pickup truck shows that the tires should be rotated every 7,500 miles and that the oil filter should be replaced every 5,000 miles. What is the lowest mileage at which both services are due at the same time? To find the answer you can use least common multiples.

Course Least Common Multiple A multiple of a number is a product of that number and a whole number. Some multiples of 7,500 and 5,000 are as follows: 7,500: 7,500, 15,000, 22,500, 30,000, 37,500, 45,000,... 5,000: 5,000, 10,000, 15,000, 20,000, 25,000, 30,000,... A common multiple of two or more numbers is a number that is a multiple of each of the given numbers. So 15,000 and 30,000 are common multiples of 7,500 and 5,000.

Course Least Common Multiple The least common multiple (LCM) of two or more numbers is the common multiple with the least value. The LCM of 7,500 and 5,000 is 15,000. This is the lowest mileage at which both services are due at the same time.

Find the least common multiple (LCM). Additional Example 1: Using a List to Find the LCM Course Least Common Multiple A. 2, 7 2: 2, 4, 6, 8, 10, 12, 14 7: 7, 14, 21, 28, 35 The LCM is 14. List some multiples of each number. Find the least value that is in both lists. B. 3, 6, 9 3: 3, 6, 9, 12, 15, 18, 21 6: 6, 12, 18, 24, 30 9: 9, 18, 27, 36, 45 The LCM is 18. List some multiples of each number. Find the least value that is in all the lists.

Try This: Example 1 Insert Lesson Title Here Course Least Common Multiple Find the least common multiple (LCM). A. 3, 7 3: 3, 6, 9, 12, 15, 18, 21 7: 7, 14, 21, 28 The LCM is 21. List some multiples of each number. Find the least value that is in both lists. B. 2, 6, 4 2: 2, 4, 6, 8, 10, 12, 14 6: 6, 12, 18 4: 4, 8, 12 The LCM is 12. List some multiples of each number. Find the least value that is in all the lists.

Find the least common multiple (LCM). Additional Example 2A: Using Prime Factorization to Find the LCM Course Least Common Multiple A. 60, = 2 · 2 · 3 · 5 Write the prime factorization of each number. 130 = 2 · 5 · 13 2, 2, 3, 5, 13 Circle the common prime factors. List the prime factors, using the circled factors only once. 2 · 2 · 3 · 5 · 13 Multiply the factors in the list. The LCM is 780.

Additional Example 2B: Using Prime Factorization to Find the LCM Course Least Common Multiple Find the least common multiple (LCM). B. 14, 35, = 2 · 7 Write the prime factorization of each number. 35 = 5 · 7 2, 5, 7, 7 Circle the common prime factors. List the prime factors, using the circled factors only once. 2 · 5 · 7 · 7 Multiply the factors in the list. The LCM is = 7 · 7

Try This: Example 2A Insert Lesson Title Here Course Least Common Multiple Find the least common multiple (LCM). A. 50, = 2 · 5 · 5 Write the prime factorization of each number. 110 = 2 · 5 · 11 2, 5, 5, 11 Circle the common prime factors. List the prime factors, using the circled factors only once. 2 · 5 · 5 · 11 Multiply the factors in the list. The LCM is 550.

Try This: Example 2B Insert Lesson Title Here Course Least Common Multiple B. 18, 36, = 2 · 3 · 3 Write the prime factorization of each number. 36 = 2 · 2 · 3 · 3 2, 2, 3, 3, 3 Circle the common prime factors. List the prime factors, using the circled factors only once. 2 · 2 · 3 · 3 · 3 Multiply the factors in the list. The LCM is = 2 · 3 · 3 · 3

Mr. Washington will set up the band chairs all in rows of 6 or all in rows of 8. What is the least number of chairs he will set up? Additional Example 3: Application Course Least Common Multiple Find the LCM of 6 and 8. 6 = 2 · 3 8 = 2 · 2 · 2 The LCM is 2 · 2 · 2 · 3 = 24. He will set up at least 24 chairs.

Try This: Example 3 Insert Lesson Title Here Course Least Common Multiple Two satellites are put into orbit over the same location at the same time. One orbits the earth every 24 hours, while the second completes an orbit every 18 hours. How much time will elapse before they are once again over the same location at the same time? 24 = 2 · 2 · 2 · 3 18 = 2 · 3 · 3 The LCM is 2 · 2 · 2 · 3 · 3 = 72. Find the LCM of 24 and 18.

Lesson Quiz Find the least common multiple (LCM) , , 6, You are planning a picnic. You can purchase paper plates in packages of 30, paper napkins in packages of 50, and paper cups in packages of 20. What is the least number of each type of package that you can buy and have an equal number of each? Insert Lesson Title Here Course Least Common Multiple 2. 24, , 8, packages of plates 6 packages of napkins 15 packages of cups