Question

The LCM and product of two numbers X and Y are 180 and 2700, respectively. If X is completely divisible by Y, then the value of (X-Y) is _____.

• A. 132
• B. 195
• C. 180
• D. 165
• E. 182

Answer 1

Answer: (D)

165

Answer 2

HCF of X and Y =$\frac{product}{LCM}=\frac{2700}{180}=15$
Let Y = 15a and given X is completely divisible by Y, then
X = 15ab
For HCF of X and Y to be 15, a must be 1.
So, X = 15b and Y = 15
Now, product of two numbers = 2700
15b × 15 = 2700
⇒ b = 12
So, (X – Y) = 15(12 – 1) = 15 × 11 = 165.
So, The correct option is (D) : 165.