Question 1

Explanation

We are given three different land areas: $120\text{ m}^2$, $180\text{ m}^2$, and $240\text{ m}^2$. The goal is to divide these lands into plots of equal size, maximizing the area of each plot.

This problem can be solved by finding the Greatest Common Divisor (GCD) of the three numbers. The GCD will give us the largest value that evenly divides all three land areas.

First, we perform prime factorization for each area:

To determine the GCD, we take the common prime factors with the lowest exponent:

• Factor 2: the lowest exponent is $2^2$.
• Factor 3: the lowest exponent is $3^1$ (or 3).
• Factor 5: the lowest exponent is $5^1$ (or 5).

Thus, the GCD is:

Therefore, the largest possible area for each plot of land is $60\text{ m}^2$.