1. Writing Improper Fractions EXAMPLE 1 Using the Least Common Multiple EXAMPLE 1 Model Trains Two model trains share a station, but they run on separate tracks. One of the trains returns to the station every 4 minutes. The other returns every 6 minutes. Both trains just left the station. When will the trains next return to the station at the same time?

2. Writing Improper Fractions EXAMPLE 1 You can find when the model trains described above will return to the station at the same time by finding the least common multiple of 4 and 6. Begin by writing the multiples of 4 and 6. Then identify any common multiples. 12, 24, and 36 are common multiples, so the LCM is 12. The trains will both return to the station in 12 minutes. ANSWER Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36,... Multiples of 6 : 6, 12, 18, 24, 30, 36,... Using the Least Common Multiple

3. Writing Improper Fractions EXAMPLE 1 Finding the Least Common Multiple EXAMPLE 2 ANSWER The least common multiple of 7 and 8 is 56. Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56,... Find the least common multiple of 7 and 8 by using a list. Multiples of 8 : 8, 16, 24, 32, 40, 48, 56,...

4. GUIDED PRACTICE for Examples 1 and 2 Find the LCM of the numbers by listing multiples. 1. 3, 5 ANSWER 15 2. 12, 16 ANSWER 48 3. 9, 10 ANSWER 90 4. 2, 6, 14 ANSWER 42 5. 15, 20 ANSWER 60 6. 7, 11 ANSWER 77 7. 3, 12, 15 ANSWER 60 8. 21, 84 ANSWER 84