Question 134110
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*5*5}}}
{{{360 = 2*2*2*3*3*5}}}
Now where you have repeated factors, write them in exponential form:
{{{75 = 2*5^2}}}
{{{360 = 2^3*3^2*5}}}
Then, from each list, select the highest power of each factor and multiply these together to get the LCM:
{{{LCM = 2^3*3^2*5^2}}}
{{{LCM = 1800}}}
Answer: 1800 movements will be needed for the sector to land in its original position.