There is a factory that makes widgets in different colors. The production time for each color is different. At the end of each day, all the widgets produced that day are placed in boxes. On a certain day, the factory made 1,680 green widgets and 8,640 purple widgets. It takes 12 minutes to produce a batch of green widgets and 45 minutes to produce a batch of purple widgets. Determine the answer to the following question: “In a factory, if both colors of widgets start production at the same time and run continuously, after how many minutes will their starting time align again?” Explain the steps and problem-solving strategy used to determine the answer. 1. Explain why the final answer is a greatest common divisor, least common multiple, or neither.
| There is a factory that makes widgets in different colors. The production time for each color is different. At the end of each day, all the widgets produced that day are placed in boxes. On a certain day, the factory made 1,680 green widgets and 8,640 purple widgets. It takes 12 minutes to produce a batch of green widgets and 45 minutes to produce a batch of purple widgets. |
Determine the answer to the following question: “In a factory, if both colors of widgets start production at the same time and run continuously, after how many minutes will their starting time align again?” Explain the steps and problem-solving strategy used to determine the answer.
1. Explain why the final answer is a greatest common divisor, least common multiple, or neither.
Given
There is a factory that makes widgets in different colors. The production time for each color is different.
At the end of each day, all the widgets produced that day are placed in boxes.
On a certain day, the factory made 1,680 green widgets and 8,640 purple widgets.
It takes 12 minutes to produce a batch of green widgets and 45 minutes to produce a batch of purple widgets.
We are required to find
In a factory, if both colors of widgets start production at the same time and run continuously, after how many minutes will their starting time align again?
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