Lesson 1.4
Least Common Factor
Goal: Find the least common multiple of two or more numbers
Example 1: Using the least common multiple
CommercialsOne TV station shows commercials every 6 minutes. Another station shows commercials every 8 minutes. For the shows that air at 7:00 A.M., at what time will both stations first play a commercial?
You can determine when both stations will first play a commercial by finding the least common multiple of 6 and 8. Begin by writing the multiples of 6 and 8. Then identify any common multiples.
Multiples of 6:
Multiples of 8:
Answer: The television stations will first both show a commercial in ______minutes, or at _____ A.M.
Example 2: Finding the Least Common Multiple
Find the least common multiple of 5 and 9.
Multiples of 5: ______
Multiples of 9: ______
Answer: The least common multiple of 5 and 9 is ______.
Guided Practice: Find the least common multiple of the numbers by listing.
- 4,7
7: 7, 14, 21, 28
LCM = 28 /
- 5, 10
- 3, 12
- 2, 6
- 2, 10
- 8, 12
Example 3: Using the Least Common Multiple
Fitness Center: All classes at the fitness center start at 6 A.M. The water aerobics class repeats every 60 minutes. The power yoga class repeats every 45 minutes. The circuit training class repeats every 90 minutes. What is the next time that all three classes start at the same time?
Solution
Find the least common multiple of 60, 45, and 90.
60 = 45 = 90 =
The least common multiple is ______.
Answer: The classes start at the same time again in _____ minutes, or ____ hours, after 6 A.M., which is _____ A.M.
Practice: Find the LCM of the numbers by listing multiples.
- 9, 12
- 4, 9
- 5, 20
- 2, 10
- During the summer, you mow lawns for extra money. One customer pays you to mow the lawn every 6 days and another customer pays you to mow the lawn every 9 days. If you mow the lawns today, in how many days will you mow both lawns again on the same day? If today is Monday, on what day of the week will you mow both lawns again on the same day?
- At an animal rehabilitation center, the baby rabbits need to be fed every 8 hours and the baby squirrels need to be fed every 6 hours. If the rabbits and squirrels are both fed at 9:30 A.M., when will they be fed again at the same time?