Question

The LCM and HCF of two numbers are equal, then the numbers must be

• A. Composite
• B. Prime
• C. Equal
• D. Co-prime

Answer 1

The correct option is C Equal

Let the numbers be x and y.
Now, given that LCM(x, y) = HCF(x, y).
Let LCM(x, y) = HCF(x, y) = k
HCF being the highest common factor is always a factor of both the numbers.
Therefore, the numbers can be written as multiples of HCF.
i.e. x = ka and y = kb for some natural numbers a and b ..…(1)
Now, since the product of two numbers is equal to the product of their LCM and HCF, we have
x × y = LCM(x, y) × HCF(x, y)
⇒ ka × kb = k × k
⇒ ab = 1
As a and b are natural numbers, therefore, a = 1 and b = 1.
Substituting a = 1 and b = 1 in (1), we get x = k and y = k.
Thus, if the HCF and LCM of the two numbers are equal, then the numbers must be equal.
Hence, the correct answer is option (c).