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Wire cut into 3 equal parts

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Wire cut into 3 equal parts

by Osirus@VeritasPrep » Sun Feb 07, 2010 5:18 pm
A wire is cut into 3 equal parts. The resulting segments are then cut into 4, 6, and 8 equal parts, respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire?

I understand the explanation in my book (Kaplan Premier), my question is how was I supposed to recognize that this was a LCM problem? How can I recognize that these types of problems are testing LCM in the future?

If you're going to post the solution without addressing the specific questions I had just to pad your post count, please don't respond. Thanks in advance.
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by ajith » Sun Feb 07, 2010 8:02 pm
osirus0830 wrote:A wire is cut into 3 equal parts. The resulting segments are then cut into 4, 6, and 8 equal parts, respectively. If each of the resulting segments has an integer length, what is the minimum length of the wire?

I understand the explanation in my book (Kaplan Premier), my question is how was I supposed to recognize that this was a LCM problem? How can I recognize that these types of problems are testing LCM in the future?

If you're going to post the solution without addressing the specific questions I had just to pad your post count, please don't respond. Thanks in advance.
Another approach to solve this problem may be to move logically
The least sized wire has 8 equal parts and say length of 1; then it is not possible for the 6 parts to have integer length
for 6 parts to have integer length 8 parts should be at least a multiple of 3. 3 is the least multiple of 3

Try that - 8*3; 6*4 and 4*6 - perfect!

I am not suggesting to solve in this method, but it will give you an insight how this becomes an LCM problem
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