Problem involving relative measurements

[courtrigrad]

Hello all

I need help with the following problem:

Two measuring sticks use the same unit but the scale on one stick has 635 marks per unit and the scale on the other stick has 465 marks per unit. Suppose the sticks are placed together so that the 0 mark on each scale line up. What is the number of the next mark on the 465 scale that lines up exactly with a mark on the 635 scale?

I know that the the 635 scale is 635 / 465 times longer than the second scale. How would I find the mark?

Any help is greatly appreciated

Thanks

[courtrigrad]

any help is appreciated!

[chronon]

You want the smallest integer N>0 such that N/465=M/635 for some integer M>0

So N*635=M*465 is the least common multiple of 465 and 635

[HallsofIvy]

The simplest way to find the "least common multiple" is to factor the two numbers:
465= 3*5*31 and 635= 5*127. Any multiple of both must have each of those as factors: 3*5*31*127.

[mathwonk]

the simplest but also the slowest. quicker is of course euclid's algorithm, perhaps the first person to record this problem and its solution.

[courtrigrad]

How would you implement Euclid;s algorithm to solve this problem?

Thanks