Question

If the HCF of two numbers is 126, then their LCM can be

• A. 189
• B. 315
• C. 252
• D. 441

Answer 1

The correct option is C 252

Let the two numbers be x and y.
HCF of x and y is 126.
∴ x = 126a and y = 126b, where HCF of a and b is 1.
As, Product of two numbers = Product of HCF and LCM.
$\Rightarrow x\times y=126\times \mathrm{LCM}$
$\Rightarrow 126a\times 126b=126\times \mathrm{LCM}$

$\Rightarrow \mathrm{LCM}=126\mathrm{ab}$

⇒ 126 is a factor of LCM.

Therefore, LCM can be 126, 252, 378, 504, ...

Hence, the correct answer is option (c).