Integer is a fundamental concept in GRE. Refer to https://gre.myprepclub.com/forum/math-lesson-integer-2620.html

The question tells us that a given wire is equally cut into three parts and each of those three parts are further cut into 4,6 and 8 parts. We are required to find the original length of the wire if each of those parts is a +ve integer.

Answer is 72
3 equal parts must be =24,24,24

Why are we using the least common multiple? Can someone explain in more depth?

Why 24?

Let N be the length of the wire
Since the wire is cut into 3 equal parts
So N/3, N/3, N/3 are the 1st partitions
Again, The resulting segments are divided into 4,6,8 parts respectively
Let x, y, z be the length of the each 4,6,8 segment partition respectively
From the given data, 4x+6y+8z=N
Also, 4x = 6y = 8z = N/3
Then 3*4x=N implies x= N/12, y = N/18, z= N/24, Also x,y,z must be integers
We have to take LCM of (12,18,24) = 72 which is the possible value of N

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