Question

If the LCM of three numbers is 9570, then their HCF is

• A. $11$
• B. $12$
• C. $19$
• D. $21$

Answer 1

Answer: (A)

$11$

Let us first take the three numbers as $9570,1$ and $1$, then

LCM $=9570,$ HCF $=1$

Now let us take numbers as $9570,9570$ and $9570$.

LCM $=9570,$ HCF $=9570$

But in the given question, choices have already been given and we are supposed to eliminate values which can not be HCF.

Now , the prime factorization of $9570$ is as follows:

$9570=2\times 3\times 5\times 11\times 29$

Since, we know that HCF must always be a factor of LCM. Therefore, from the given choices in the question itself, only $11$ can be the HCF.

Hence, HCF is $11$