Section 3.2 Least Common Multiple 173 Skill Practice Find the LCM by using division by prime factors. 7. 20, 36, and 15 Answer 7. 180 3. Finding the LCM by Using Division by Primes We present a third method for finding least common multiples. We systematically divide by prime numbers to determine which will be a factor of the LCM. This method is particularly helpful if three or more numbers are involved. Finding the LCM by Using Division by Primes Example 3 Find the LCM of 32, 48, and 30 by using division of prime factors. Solution: To begin this process, find any prime number that divides evenly into any of the numbers.Then divide and write the quotient as shown.We begin by dividing by the smallest prime number, 2. 2232 48 30 16 24 15 Repeat this process and bring down any number that is not divisible by the chosen prime. Bring down the 15. 2232 48 30 2216 24 15 28 12 15 Continue until all quotients are 1. The LCM is the product of the prime factors at the left. At this point, the prime number 2 does not divide evenly into any of the quotients.We try the nextgreater prime number, 3. 2232 48 30 2216 24 15 228 12 15 224 6 15 222 3 15 321 3 15 521 1 5 1 1 1 The LCM is 2 2 2 2 2 3 5 480. TIP: We have presented three methods to find the LCM. Try each method. Then you and your instructor can decide which methods work best for you. 4. Applications of the LCM Using the LCM in an Application Example 4 A tile wall is to be made from 6-in., 8-in., and 12-in. square tiles. A design is made by alternating rows with different-size tiles. The first row uses only 6-in. tiles, the second row uses only 8-in. tiles, and the third row uses only 12-in. tiles. Neglecting the grout seams, what is the shortest length of wall space that can be covered using only whole tiles?
miller_basic_college_math_3e_ch1_3
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