The difference of two numbers is \( \frac{1}{5} \) of their sum, and their sum is 45. Find the LCM.

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  1. 45
  2. 36
  3. 54
  4. 27

Answer (Detailed Solution Below)

Option 3 : 54
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Detailed Solution

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Given:

The difference of two numbers is \(\dfrac{1}{5}\) 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 = \(\dfrac{1}{5}\) ×  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).

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