We need to find What is the greatest possible common divisor(GCD) of two different positive integers which are less than 144

Let's solve it using two methods

Method 1: Logic

Now the numbers are less than 144
=> We can take the numbers as 142 and 143, but then their GCD = 1 as they will have only 1 as the common factor.

If we think about this then we will realize that we can take two numbers such that one number is a big number (lets say x) *1 and other is a big number (lets say x) * 2
=> \(\frac{144}{2}\) = 72 can be taken as x and the numbers can be taken as 72*1 = 72 and 72*2 = 144

But, the numbers have to be less than 144
=> We can try with \(\frac{142}{2}\) = 71 and 71*2 = 142

So, Answer will be D

Method 2: Eliminate Option Choices

A. 143 For GCD of two different numbers to be 143 both have to be multiple of 143
=> We can take the numbers as 143*1 and 143*2 = 286, but numbers CANNOT be ≥ 144 => NOT POSSIBLE

B. 142 For GCD of two different numbers to be 142 both have to be multiple of 142
=> We can take the numbers as 142*1 and 142*2 = 284, but numbers CANNOT be ≥ 144 => NOT POSSIBLE

C. 72 For GCD of two different numbers to be 72 both have to be multiple of 72
=> We can take the numbers as 72*1 and 72*2 = 144, but numbers CANNOT be ≥ 144 => NOT POSSIBLE

D. 71 For GCD of two different numbers to be 71 both have to be multiple of 71
=> We can take the numbers as 71*1 and 71*2 = 142, which are both < 144 => POSSIBLE

So, Answer will be D
Hope it helps!

To learn more about LCM and GCD watch the following videos