Question
Download Solution PDFThe difference of two numbers is \( \frac{1}{5} \) of their sum, and their sum is 45. Find the LCM.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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