The difference of two numbers is  of their sum, and their sum is 45. Find the LCM.

Given:

The difference of two numbers is of their sum, and their sum is 45.

Calculation:

Let the two numbers be x and y.

x - y = 1/5 (x + y)

x - y =  ×  45

⇒ x - y = 9 

We have the equations:

x + y = 45

x - y = 9

Adding these equations:

⇒ 2x = 54 ⇒ x = 27

So, y = 18

Now, we find the LCM of 27 and 18.

Prime factorization of 27: 3³

Prime factorization of 18: 2 × 3²

LCM = 2 × 3³ = 54

∴ The correct answer is option (3).