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Determine the largest number of widgets that can be placed in each box if it is required that all boxes contain the same number of widgets and each box contains only one color. 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 1,260 red widgets and 4,032 blue widgets. It takes 18 minutes to produce a batch of red widgets and 32 minutes to produce a batch of blue widgets.