Question

If the LCM of three numbers is 9570, then their HCF is?
A. 11
B. 12
C. 19
D. 21

Answer 1

Hint: We need to solve this question on a logical basis. Here, to find this question first we need to know the relationship between LCM & HCF with the help of an example. As HCF is the factor of LCM, we need to check from the options which are the factor of LCM to find HCF.

Complete step by step solution:
Here, it is given that LCM $=9570$
The LCM stands for lowest common multiple, the least common multiple of any two or more given natural numbers are termed as LCM.
For example:
The LCM of $12,15\And 18$ is 180.
Here the common factor of $12,15\And 18$ is ‘3’. So, HCF of $12,15\And 18$ is 3.
Where, HCF is the highest common factor of any two or more given natural numbers.
Here, we can also observe that 3 is also a factor of 180, so we can say that HCF is one of the factors of LCM.
Here in this question we are given with the LCM $=9570$ .
We know that the HCF is always a factor of LCM. So, the prime factors of 9570 are –
$\begin{align}
  & 2\left| \!{\underline {\,
  9570 \,}} \right. \\
 & 3\left| \!{\underline {\,
  4785 \,}} \right. \\
 & 5\left| \!{\underline {\,
  1595 \,}} \right. \\
 & 11\left| \!{\underline {\,
  319 \,}} \right. \\
 & 29\left| \!{\underline {\,
  29 \,}} \right. \\
 & \text{ 1} \\
\end{align}$
$9570=2\times 3\times 5\times 11\times 29$
From the given choices in the question itself, only 11 is the factor of 9570.
So, HCF will be 11.
Therefore, HCF of the LCM 9570 is 11.
Hence, option (A) is the correct answer.

Note: Students should be very careful while solving such types of tricky questions. As the data given in the question is not much sufficient, we can solve this directly by taking the data from the options. Here, from the options only 11 is the factor of 9570 so, option (A) will be the correct answer.