1 Find the Least Common Multiple (LCM) What is a multiple? Let’s look at some multiples of 3. 1 3 3 3 is a multiple of 3. 2 3 6 6 is a multiple of 3. 3 3 9 9 is a multiple of 3. 4 3 12 12 is a multiple of 3. We fi nd multiples of 3 by multiplying 3 by natural numbers. We can also think of multiples in terms of division. Notice that every multiple of 3 is divisible by 3. So what is a least common multiple, or LCM? Definition The least common multiple, or LCM, of a group of natural numbers is the smallest natural number divisible by each number in the group. Example: The LCM of 2 and 3 is 6 because 6 is the smallest number divisible by both 2 and 3. There are different ways to fi nd the least common multiple of a group of numbers. To use the fi rst method, we begin by listing some multiples of each number. Then, the least common multiple (LCM) is the smallest number that appears on each list. Find the least common multiple of: a) 4 and 6. b) 5, 10, and 15. Solution a) List some multiples of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20, 24, … Multiples of 6: 6, 12, 18, 24, 30, 36, … (The three dots at the end of each list mean that the list continues forever in the same pattern.) Notice that two numbers appear on each list: 12 and 24. So, 12 and 24 are both common multiples of 4 and 6, but 12 is the least common multiple (LCM) because it is the smallest number on each list. b) List some multiples of 5, 10, and 15. Multiples of 5: 5, 10, 15, 20, 25, 30, … Multiples of 10: 10, 20, 30, 40, 50, 60, … Multiples of 15: 15, 30, 45, 60, 75, 90 … The LCM of 5, 10, and 15 is 30 because it is the smallest number that appears on each list. EXAMPLE 1 230 CHAPTER 4 Adding and Subtracting Fractions www.mhhe.com/messersmith
messersmith_power_basic_college_1e_ch4_7_10
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