Problem Solving

Here's the question:

A wire is cut into three 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?

a) 24
b) 36
c) 48
d) 54
e) 72

I would think (4+6+8) * 3= 54 would be the correct answer.

But you have to take the LCM of 4,6,8 and you would get 24, and then you would multiply 24 *3= 72. Why would you do the LCM? I have a hard time visualizing this.

There are 2 pieces here, first is cutting into 3 equal parts and then splitting those into 4:6:8 ratio, and the questions asks for minimum length, so you'll have to take LCM for those ratios which is 24. The total length of the wire is hence 24*3 = 72.

Thanks guys.

i did it in a different way.
if the wire is divided into 3 parts (x/3, x/3 and x/3) and then later divided into 4,6,8 parts (which would be equal to x/12, x/18 and x/24), pick numbers given as answers to see where all three equations will give you integers.... 72 is the only one....