Babita K. answered • 03/08/17
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Math, Science, and Writing Tutor with Lots of Experience
Hi Shelly,
Assuming that each of the movies keep running continuously cycling through, this is a question where you need to find the least common factor. In other words, what is the least common denominator for 750, 650, and 90?
Since all three numbers are multiples of 10, we can divide each by 10 to make factoring easier for us to do. Dividing by 10, we get 75, 65, and 9; so, we now need to find the least common denominator for 75, 65, and 9.
To do this, we find prime number factors of all three or at least two of the numbers:
Step a) We will start with the smallest prime number 2, which doesn't go into any of the numbers; so 2 is not a prime factor.
Step b) 3 is a prime factor of both 75 and 9. When we divide 75 and 9 by 3, we get 25 and 3, respectively. Dividing through by 3, the three numbers that we now have are 25, 65, and 3. Note that 3 doesn't go directly into 65 and so we leave it as is. The prime factor we have so far is 3.
Step c) The next prime number is 5, which goes into both 25 and 65. Dividing both 25 and 65 by 5, we get 5 and 13, respectively. Again, note that 5 doesn't go directly into 3 and so we leave it as is. The three numbers that we now have are 5, 13, and 3, which are all prime numbers. The prime factors that we divided by so far are 3 in Step (b) and 5 in Step (c).
Now, we are ready to find the least common denominator. All that we need to do is multiply the prime factors (3 and 5) and prime numbers that we ended up with (5, 13, and 3). So, the least common denominator = 3x5x5x13x3 = 2925.
Now we need to multiply 2925 by 10 to get 29250. We do this since we initially divided 750, 650, and 90 by 10 to make the divisions easier. This is much easier demoed on board, but I hope the explanation makes the process clear.
Mark M.
03/08/17