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Finding the LCM by Listing Multiples
The listing multiples method is a straightforward way to find the least common multiple of two numbers without using prime factorizations. The procedure has three steps:
- List several multiples of each number — write out the first several products of each number with the counting numbers (e.g., for : ; for : ).
- Identify the smallest number that appears in both lists — scan the two lists for common entries and select the least one.
- That number is the LCM.
This approach works well when the numbers are small enough that their multiples can be listed quickly. For larger numbers or cases where common multiples are not immediately obvious, the prime factors method is often more efficient.
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Finding the LCM Using the Prime Factors Method
Least Common Denominator
Finding the LCM by Listing Multiples
Finding the Least Common Multiple Using the Prime Factors Method
A logistics manager needs to align two different shipping schedules: one that repeats every 10 days and another that repeats every 15 days. To find the first day both shipments will arrive at the same time, the manager looks for the smallest number that is a multiple of both 10 and 15. What is the mathematical term for this value?
A technician needs to find the first time two different maintenance cycles will overlap. Arrange the steps for finding the Least Common Multiple (LCM) using the listing method in the correct order.
In a facility management plan, the Least Common Multiple (LCM) of two different service cycles is defined as the ____ number that is a multiple of both cycle lengths.
A warehouse manager is coordinating two recurring delivery schedules: one that arrives every 6 days and another that arrives every 8 days. The manager assumes that the Least Common Multiple (LCM) is 48 because 6 multiplied by 8 equals 48. Is this assumption True or False based on the definition of the Least Common Multiple?
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A maintenance supervisor is coordinating the service schedules for two different pieces of equipment: a generator that is serviced every 8 days and a cooling system that is serviced every 12 days. Match each mathematical term with the description that best explains its role in identifying when these maintenance tasks will overlap.
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A maintenance supervisor is training a new hire on how to synchronize equipment service intervals. For two machines with service cycles of 8 hours and 12 hours, the new hire suggests that the Least Common Multiple (LCM) is 4 hours. Is this suggestion mathematically possible based on the definition of a multiple?
An office manager is coordinating two recurring maintenance tasks: a printer service every 6 weeks and a carpet cleaning every 8 weeks. The manager identifies that both tasks will fall on the same week at the 24-week, 48-week, and 72-week marks. Based on the mathematical definition of the Least Common Multiple (LCM), which of these intervals represents the LCM for the two tasks?
Learn After
A project manager is using the 'listing multiples' method to find the next day two recurring office tasks will overlap. Arrange the steps of this method in the correct order from start to finish.
An operations manager is choosing a method to find the least common multiple for two production cycles. According to the 'listing multiples' method description, when is this specific approach most effective to use?
A logistics coordinator is using the 'listing multiples' method to synchronize two different delivery schedules. After listing several multiples for each schedule, the coordinator identifies the Least Common Multiple by selecting the __________ number that appears in both lists.
A facilities manager is learning the 'listing multiples' method to coordinate maintenance schedules for two different pieces of equipment. Match each term of the method with its correct description in this professional context.
A maintenance supervisor is using the 'listing multiples' method to synchronize the service cycles of two different machines. True or False: According to this method, once the lists of multiples are generated, the Least Common Multiple (LCM) is found by identifying the largest number that appears in both lists.
Synchronizing Maintenance Cycles
Standard Operating Procedure: Listing Multiples
Maintenance Cycle Synchronization Protocol
A logistics manager is using the 'listing multiples' method to synchronize two delivery routes that repeat every 10 days and every 15 days. Which of the following sequences correctly demonstrates the first step of this method for the 10-day route?
A project coordinator is using the 'listing multiples' method to find when two recurring tasks will overlap. To generate the lists of multiples for each task's frequency, the coordinator should multiply each frequency by which set of numbers?