Question

If the L.C.M. of two numbers is $2520$ and H.C.F is $12$. If one number is $504$, then the other number will be:

• A. $50$
• B. $65$
• C. $40$
• D. $60$

Answer 1

The correct option is D $60$

We know that LCM$\times$HCF = product of two numbers. This formula can be applied only in the case of two numbers. However, if the numbers are relatively prime to each other (i.e., HCF of numbers $=1$), then this formula can be applied for any number.

It is given that the LCM of two numbers is $2520$ and their HCF is $12$. One of the number is $504$ and let the other number be $x$, then applying the above formula LCM$\times$HCF = product of two numbers, we get:

$2520\times 12=504\times x\Rightarrow 30240=504x\Rightarrow x=\frac{30240}{504}\Rightarrow x=60$

Hence, the other number is $60$.