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 = 3 40 = 23 5322=6052 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.

323 52 = 22 2 3 5 5 600=

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

Guided Practice

9. WHAT IF? In Example 3, suppose Tour C returns every25 minutes. In how many hours will the three tours return at the same time?

ANSWER 5 hr

for Example 3