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Writing Improper Fractions EXAMPLE 1 Using Prime Factorization to Find the LCM EXAMPLE 3 Find the LCM of 84 and 360 using prime factorization. STEP 1 Begin by writing the prime factorization of each number. 84 = =

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Writing Improper Fractions EXAMPLE 1EXAMPLE 3 STEP 2 Circle the common factors. Then multiply the common factors (one for each pair) and all the uncircled factors = = The least common multiple of 84 and 360 is ANSWER Using Prime Factorization to Find the LCM

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Writing Improper Fractions EXAMPLE 1 Using the Least Common Multiple EXAMPLE 4 Tour Bus Schedules Three tour buses leave the visitors center at 9:00 A.M. Bus A returns to the visitors center every 60 minutes, Bus B returns every 40 minutes, and Bus C returns every 75 minutes. What is the next time the buses will all return to the visitors center at the same time?

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Writing Improper Fractions EXAMPLE 1EXAMPLE 4 SOLUTION Find the least common multiple of 60, 40, and = = The least common multiple is = 60 = The buses all return at the same time in 600 minutes, or 10 hours, after 9:00 A.M., which is 7:00 P.M. ANSWER Using the Least Common Multiple

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EXA GUIDED PRACTICE for Examples 3 and 4 Find the LCM of the numbers using prime factorization. 9.36, 72 ANSWER , 30 ANSWER , 126 ANSWER , 22, 55 ANSWER 220

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EXA GUIDED PRACTICE ANSWER 12 noon for Examples 3 and 4 In Example 4, suppose Bus A returns every 30 minutes, Bus B returns every 20 minutes, and Bus C returns every 45 minutes. What is the next time the buses will all return at the same time to the visitors center? What If? 13.

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