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EXAMPLE 1

Animal Clinic. A veterinarian at an animal clinic is on call every four days. Today is Saturday, and the veterinarian is on call. In how many more days will the veterinarian be on call on a Saturday again?. EXAMPLE 1. Finding the Least Common Multiple. SOLUTION.

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EXAMPLE 1

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  1. Animal Clinic A veterinarian at an animal clinic is on call every four days. Today is Saturday, and the veterinarian is on call. In how many more days will the veterinarian be on call on a Saturday again? EXAMPLE 1 Finding the Least Common Multiple SOLUTION The veterinarian is on call every 4 days. A Saturday occurs every 7 days. Find the least common multiple of 4 and 7.

  2. METHOD 1 Use a calendar. Start with a Saturday and circle every 4 days on a calendar. You can see that the veterinarian will be on call on a Saturday in 28 days. EXAMPLE 1 Finding the Least Common Multiple

  3. 4, 8, 12, 16, 20, 24, 28, 32, . . . Multiples of 4: 7, 14, 21, 28, 35, 42, 49, 56, . . . Multiples of 7: EXAMPLE 1 Finding the Least Common Multiple METHOD 2 Make a list. List the multiples of each number. The least common multiple is the first number that appears in both lists. The LCM of 4 and 7 is 28.

  4. 4 = 22 7 = 7 4 = 22 7 = 7 = 28 22 7 EXAMPLE 1 Finding the Least Common Multiple METHOD 3 Use prime factorization. Write the prime factorization of each number. Circle the greatest power of each prime factor. The LCM of 4 and 7 is the product of the circled numbers:

  5. ANSWER In 28 days, the veterinarian will be on call on a Saturday. EXAMPLE 1 Finding the Least Common Multiple

  6. STEP 1 Write the prime factorization of each number and circle the greatest power of each prime factor. = 25 32 = 25 3 = 23 3 5 96 120 EXAMPLE 2 Finding the Least Common Multiple Find the LCM of 32, 96, and 120 using prime factorization. SOLUTION

  7. ANSWER 25 3 5 The LCM of 32, 96, and 120 is 480. EXAMPLE 2 Finding the Least Common Multiple Find the product of the circled factors. STEP 2 = 480

  8. Factor each expression using exponents and circle the greatest power of each factor. STEP 1 9x4z = 32x4z 6x2y = 2 3 x2y Find the product of the circled factors. STEP 2 2 32x4y z = 18x4yz EXAMPLE 3 Finding the LCM of Monomials Find the LCM of 6x2yand 9x4z. SOLUTION

  9. ANSWER The LCM of 6x2y and 9x4z is 18x4yz. EXAMPLE 3 Finding the LCM of Monomials

  10. ANSWER In 21 days, the veterinarian will be on call on a Saturday. for Examples 1,2 and 3 GUIDED PRACTICE 1. What If? In Example 1, suppose the veterinarian is on call every 3 days. In how many more days will the vet be on call on a Saturday again?

  11. for Examples 1,2 and 3 GUIDED PRACTICE Find the least common multiple of the numbers. 2.6, 15

  12. ANSWER The LCM of 6 and 15 is 30. for Examples 1,2 and 3 GUIDED PRACTICE

  13. for Examples 1,2 and 3 GUIDED PRACTICE 3.4, 20

  14. ANSWER The LCM of 4 and 20 is 20 for Examples 1,2 and 3 GUIDED PRACTICE

  15. for Examples 1,2 and 3 GUIDED PRACTICE 4.12, 28

  16. ANSWER The LCM of 12 and 28 is 84. for Examples 1,2 and 3 GUIDED PRACTICE

  17. for Examples 1,2 and 3 GUIDED PRACTICE 5.24, 36, and72

  18. ANSWER The LCM of 24, 36 and 72 is 72. for Examples 1,2 and 3 GUIDED PRACTICE

  19. for Examples 1,2 and 3 GUIDED PRACTICE 6. 8x3, 20x7

  20. ANSWER The LCM of 8x3and 20x7is 40x7. for Examples 1,2 and 3 GUIDED PRACTICE

  21. for Examples 1,2 and 3 GUIDED PRACTICE 7. 12y4, 36y8

  22. ANSWER The LCM of 12y4and 36y8is 36y8. for Examples 1,2 and 3 GUIDED PRACTICE

  23. for Examples 1,2 and 3 GUIDED PRACTICE 8. 4ab2, 10a2b

  24. ANSWER The LCM of 4b2and 10a2bis 20a2b2. for Examples 1,2 and 3 GUIDED PRACTICE

  25. for Examples 1,2 and 3 GUIDED PRACTICE 9. 6m3np2, 8mp3

  26. ANSWER The LCM of 6m3np2and 8mp3is 24m3np3. for Examples 1,2 and 3 GUIDED PRACTICE

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