# 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?

Oct 22, 2015

$72$ units of length

#### Explanation:

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

Then $n$ is divisible by $4 = 2 \cdot 2$, $6 = 2 \cdot 3$ and $8 = 2 \cdot 2 \cdot 2$.

As a result, $n$ must be divisible by $2 \cdot 2 \cdot 2 \cdot 3 = 24$

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