1. 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 =

2. 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

3. 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?

4. 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

5. 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

6. 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