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?

Question

4603 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-22T19:51:10

#72# units of length

Suppose the initial length of the wire is #3n#

Then #n# is divisible by #4 = 2*2#, #6 = 2*3# and #8 = 2*2*2#.

As a result, #n# must be divisible by #2*2*2*3 = 24#

So the total original length of the wire must be divisible by #3*24 = 72#, giving a minimum length of #72#.