Math Help - Help with looping films please!

1. Help with looping films please!

Hi, I'm an artist and want to work out how to synchronise 3 looped films with different durations.

For example, Film 1 is 100 frames long, Film 2 is 150 frames long, and Film 3 is 200 frames long. If they start playing at the same time, the point at which they synchronise is at 600 frames, when they have looped 6, 4 and 3 times respectively.

So far so simple. But the films I have don't have simple durations - one might have 183 frames, another 5669 frames, etc. How can I calculate when they will synchronise?

Any help will be gratefully received; I'll even send you a link to the finished artwork!

2. Re: Help with looping films please!

Originally Posted by yearling
Hi, I'm an artist and want to work out how to synchronise 3 looped films with different durations.

For example, Film 1 is 100 frames long, Film 2 is 150 frames long, and Film 3 is 200 frames long. If they start playing at the same time, the point at which they synchronise is at 600 frames, when they have looped 6, 4 and 3 times respectively.

So far so simple. But the films I have don't have simple durations - one might have 183 frames, another 5669 frames, etc. How can I calculate when they will synchronise?

Any help will be gratefully received; I'll even send you a link to the finished artwork!
You want to find the Lowest Common Denominator of the films. You did this in your first example by finding the LCD of 100,150 and 200 which is 600.

Prime factors are the simplest way to find out LCDs so if we split 100, 150 and 200 into it's prime factors we get:

$100 = 2^2 \cdot 5^2$
$150 = 2 \cdot 3 \cdot 5^2$
$200 = 2^3 \cdot 5^2$

To find the LCD multiply the highest powers of each number. In this case $5^2 \cdot 3 \cdot 2^3 = 600$

The prime factors of 183 and 5669 are:

183: $3 \cdot 61$
5669: $5669$ (5669 is prime)

Can you work out the LCD?

Spoiler:
To find out a number's prime factors you can divide through by the prime numbers until you reach a prime. For example 183 does not divide by 2 so we try 3. 3 does divide so divide 183 by 3 and you get 61 which is prime. Hence 3 and 61 are prime factors.

To check if a number is prime check all the numbers upto it's square root

$\sqrt{5669} \approx 75$. This will take a while so I suggest using a computer if you don't need to show your working!

3. Re: Help with looping films please!

3 x 61 x 5669 = 1037427

That's so helpful! I would never have worked it out by myself.

Thanks again.

4. Re: Help with looping films please!

Originally Posted by yearling