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A factory produces two types of widgets. The first type is produced every 12 day

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Question: A factory produces two types of widgets. The first type is produced every 12 days and the second every 15 days. How often will both types be produced on the same day? (2023)

Options:

  1. 30 days
  2. 60 days
  3. 45 days
  4. 75 days

Correct Answer: 45 days

Exam Year: 2023

Solution: 

The LCM of 12 and 15 is 60, so both types will be produced on the same day every 60 days.

A factory produces two types of widgets. The first type is produced every 12 day

Practice Questions

Q1
A factory produces two types of widgets. The first type is produced every 12 days and the second every 15 days. How often will both types be produced on the same day? (2023)
  1. 30 days
  2. 60 days
  3. 45 days
  4. 75 days

Questions & Step-by-Step Solutions

A factory produces two types of widgets. The first type is produced every 12 days and the second every 15 days. How often will both types be produced on the same day? (2023)
  • Step 1: Identify the production cycle of each type of widget. The first type is produced every 12 days, and the second type is produced every 15 days.
  • Step 2: To find out when both types will be produced on the same day, we need to calculate the Least Common Multiple (LCM) of 12 and 15.
  • Step 3: List the multiples of 12: 12, 24, 36, 48, 60, 72, ...
  • Step 4: List the multiples of 15: 15, 30, 45, 60, 75, ...
  • Step 5: Find the smallest number that appears in both lists of multiples. The smallest common multiple is 60.
  • Step 6: Conclude that both types of widgets will be produced on the same day every 60 days.
  • Least Common Multiple (LCM) – The LCM of two numbers is the smallest number that is a multiple of both.
  • Divisibility – Understanding how numbers divide into each other is crucial for finding the LCM.
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