1. 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.

2. 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 = 2 3 5  3  2 = 60 5252  5 

3. 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  2323 5252 =  2  22  3  5  5600=

4. Guided Practice for Example 3 Find the LCM of the numbers using prime factorizations. 5. 36, 72 6. 24, 30 7. 54, 126 8. 20, 22, 55 ANSWER 72 ANSWER 120 ANSWER 378 ANSWER 220 Find the LCM of the numbers using prime factorizations. 5. 36, 72

5. 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