Use prime factorization to fi nd the least common denominator of 25 36 and 17 40 , then write each fraction as an equivalent fraction with the LCD as its denominator. Solution The denominators of 25 36 and 17 40 are large, so let’s use the prime factorizations of 36 and 40 to fi nd their least common multiple. Prime factorizations: 36 2 2 3 3 40 2 2 2 5 LCM of 36 and 40: 2 2 2 3 3 5 360 The LCD of 25 36 and 17 40 is 360. Write each fraction with the LCD. 25 36 ? 360 and 17 40 ? 360 If you do not know, by inspection, what to multiply each fraction by to obtain the fraction with the LCD, go back to each prime factorization. Compare the prime factorizations of the denominators of 25 36 and 17 40 to the prime factorization of the LCD of 360 and ask yourself, “What’s missing?” Compare Compare 36 2 2 3 3 40 2 2 2 5 to to 360 2 2 2 3 3 5 360 2 2 2 3 3 5 These factors are not in 36. These factors are not in 40. What factors are in 360 that are What factors are in 360 that are missing from 36? 2 and 5 missing from 40? Two factors of 3 Because 2 5 10, multiply Because 3 3 9, multiply 25 36 10 10 250 360 17 40 9 9 153 360 to obtain an equivalent fraction to obtain an equivalent fraction with a denominator of 360. with a denominator of 360. The LCD of 25 36 and 17 40 is 360, and 25 36 250 360 and 17 40 153 360 . EXAMPLE 5 YOU TRY 5 Use prime factorization to fi nd the least common denominator of 59 84 and 41 126 , then write each fraction as an equivalent fraction with the LCD as its denominator. www.mhhe.com/messersmith SECTION 4.3 Finding the Least Common Denominator 239
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