Step 2: The LCM will contain each different factor the greatest number of times it appears in any single factorization. The LCM will contain 2, 3, and 7. Use 1 factor of 2, 3, and 7. Step 3: The LCM is the product of the factors identifi ed in Step 2. The LCM of 14 and 21 is 2 3 7 42. c) Step 1: Write the prime factorizations of 6, 15, and 27. 6 2 3 15 3 5 and 27 3 3 3 c 3 factors of 3 T T 1 factor of 5 1 factor of 2 Step 2: The LCM will contain each different factor the greatest number of times it appears in any single factorization. The LCM will contain 2, 3 3 3, and 5. Use 1 factor of 2 and 5. c Use 3 factors of 3. Step 3: The LCM is the product of the factors identifi ed in Step 2. The LCM of 6, 15, and 27 is 2 3 3 3 5 270. YOU TRY 4 Find the LCM of each group of numbers using prime factorization. a) 18 and 30 b) 15 and 21 c) 18, 54, and 60 Note It is very important that you understand the different methods for finding the least common multiple. We will use these methods to find least common denominators of fractions with unlike denominators. ANSWERS TO YOU TRY EXERCISES 1) a) 18 b) 36 2) 8 3) 60 4) a) 90 b) 105 c) 540 4.2 Exercises Do the exercises, and check your work. Objective 1: Find the Least Common Multiple (LCM) 1) In your own words, defi ne the least common multiple of a group of numbers. 2) Is this statement true or false? Explain your answer. The least common multiple of 6 and 12 is 24. Find the least common multiple of each group of numbers by inspection or by making a list of multiples of both numbers. 3) 2 and 4 4) 3 and 9 5) 3 and 12 6) 5 and 15 7) 4 and 10 8) 6 and 8 www.mhhe.com/messersmith SECTION 4.2 Least Common Multiples 233
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