TOUR SCHEDULES Using Prime Factorization to Find the LCM Three trolley tours leave from the same stop at 9 : 00 A.M. Tour A returns to the the stop every.

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Presentation transcript:

TOUR SCHEDULES Using Prime Factorization to Find the LCM Three trolley tours leave from the same stop at 9 : 00 A.M. Tour A returns to the the stop every 75 minutes, Tour B returns every 60 minutes, and Tour C returns every 40 minutes. In how many hours will all three tours return to the stop at the same time? Example 3 SOLUTION Find the least common multiple of 75, 60, and 40.

Using Prime Factorization to Find the LCM STEP 1 Find the prime factorization of each number. Example 3 STEP 2 Circle the greatest power of every prime factor that appears in any of the prime factorizations. 75 = 340 =  3  2 =  5 

Using Prime Factorization to Find the LCM ANSWER The tours all return at the same time in 600 minutes, or 10 hours. Example 3 STEP 3 Multiply the circled powers.  3  =  2  22  3  5  5600=

Guided Practice for Example 3 Find the LCM of the numbers using prime factorizations , , , , 22, 55 ANSWER 72 ANSWER 120 ANSWER 378 ANSWER 220 Find the LCM of the numbers using prime factorizations , 72

Guided Practice 9. WHAT IF? In Example 3, suppose Tour C returns every 25 minutes. In how many hours will the three tours return at the same time? ANSWER 5 hr for Example 3