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?

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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#.