At a pharmaceutical company, research equipment must be shared among the scientists. There is one microscope for every 4 scientists, one centrifuge for every 3 scientists and one freezer for every 2 scientists. If there is a total of 52 pieces of research equipment at this company, how many scientists are there?

Let’s first find out the minimum number of scientists possible. It must be divisible by 4,3, and 2. Right? (if not, say if there were 9 scientists, how do you divide the freezers among them?). In other words, the minimum possible number of scientists is the LCM of 4,3, and 2.

Now, Let’s assume the LCM (12) as the number of scientists. So we have 3 microscopes, 4 centrifuge, 6 freezers. That will be 13 pieces of equipment for 12 scientists.

12 scientists → 13 equipments

x scientists → 52 equipments

Cross multiply and there you go!

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