SOLUTION: If a 75-degree sector rotates around the center of a cirlce in 75-degree movements, how many sector movements will be needed for the sector to land in its original postition?

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Question 134110: If a 75-degree sector rotates around the center of a cirlce in 75-degree movements, how many sector movements will be needed for the sector to land in its original postition?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
What you are really asking for here is the least common multiple (LCM) of 75 and 360.
You can do this by first finding the prime factors of each of the numbers.
75+=+2%2A5%2A5
360+=+2%2A2%2A2%2A3%2A3%2A5
Now where you have repeated factors, write them in exponential form:
75+=+2%2A5%5E2
360+=+2%5E3%2A3%5E2%2A5
Then, from each list, select the highest power of each factor and multiply these together to get the LCM:
LCM+=+2%5E3%2A3%5E2%2A5%5E2
LCM+=+1800
Answer: 1800 movements will be needed for the sector to land in its original position.