The Problem:
You have two ropes, one measuring 12m and the other measuring 18m. You need to cut these ropes into smaller pieces, with each piece being of the same length. The task is to determine the maximum length that each piece can be.

Solution:
To find the maximum length of each piece, we need to find the greatest common divisor (GCD) of the two rope lengths. The GCD will give us the length of the largest piece that can be cut from both ropes without any leftover.

Finding the GCD:
To find the GCD of 12 and 18, we can use the Euclidean algorithm. This algorithm states that the GCD of two numbers can be found by repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero.

Step 1:
Divide 18 by 12: 18 ÷ 12 = 1 remainder 6

Step 2:
Divide 12 by 6: 12 ÷ 6 = 2 remainder 0

Since the remainder is zero, we stop here. The GCD of 12 and 18 is 6.

The Maximum Length:
The maximum length of each piece that can be cut from the ropes is equal to the GCD, which is 6. Therefore, each piece can be a maximum of 6m in length.

Final Answer:
The maximum length of each piece that can be cut from the ropes is 6m.