Writing Improper Fractions EXAMPLE 1 EXAMPLE 3 Using Prime Factorization to Find the LCM Writing Improper Fractions Find the LCM of 84 and 360 using prime factorization. STEP 1 Begin by writing the prime factorization of each number. 84 = 2 2 3 7 360 = 2 2 2 3 3 5

Writing Improper Fractions EXAMPLE 1 EXAMPLE 3 Using Prime Factorization to Find the LCM Writing Improper Fractions STEP 2 Circle the common factors. Then multiply the common factors (one for each pair) and all the uncircled factors. 2 2 2 3 3 5 7 = 23 32 5 7 2520 = The least common multiple of 84 and 360 is 2520. ANSWER

Writing Improper Fractions EXAMPLE 1 EXAMPLE 4 Using the Least Common Multiple Writing Improper Fractions Tour Bus Schedules Three tour buses leave the visitor’s center at 9:00 A.M. Bus A returns to the visitor’s 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 visitor’s center at the same time?

Writing Improper Fractions EXAMPLE 4 EXAMPLE 1 Using the Least Common Multiple Writing Improper Fractions SOLUTION Find the least common multiple of 60, 40, and 75. 60 = 22 3 5 40 23 5 = 75 3 52 = The least common multiple is 23 3 52 600. = 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

Find the LCM of the numbers using prime factorization. EXA GUIDED PRACTICE for Examples 3 and 4 Find the LCM of the numbers using prime factorization. 9. 36, 72 ANSWER 72 10. 24, 30 ANSWER 120 11. 54, 126 ANSWER 378 12. 20, 22, 55 ANSWER 220

EXA GUIDED PRACTICE 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 visitor’s center? What If? 13. ANSWER 12 noon