Question

HCF of two numbers is always a factor of their LCM.

• A. True
• B. False

Answer 1

The correct option is A True

Verify the given statement

HCF is a factor of both the numbers and is also the factor of their LCM.

Let us consider two numbers $6$ and $10$.

Now, Factors of $6$ are $2\times 3$

And, Factors of $10$ are $2\times 5$

$\therefore$ H.C.F of $6$ and $10$ is $2$.

$\therefore$ L.C.M of $6$ and $10$ is $2\times 3\times 5=30$.

Thus, $2$ is a factor of $30$ .

Hence, the statement “ HCF of two numbers is always a factor of their LCM” is true.