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**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 = 360 =

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**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. = = The least common multiple of 84 and 360 is 2520. ANSWER

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**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?

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**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 = = = The least common multiple is = 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

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**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

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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

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