Question

Find the LCM and HCF of 192 and 8 and verify that the multiplication of LCM and HCF is equal to the product of two numbers.

Answer 1

Hint: We need to find the HCF and LCM of 8 and 192. First, we can take the simultaneous factorisation of those two numbers to find the HCF and LCM. Then we verify if the multiplication of LCM and HCF is equal to the product of two numbers.

Complete step-by-step answer:
We need to find the LCM of 8 and 192. LCM stands for least common multiple and HCF stands for greatest common factor.
We use the simultaneous factorisation to find the GCD and LCM of 192 and 8.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 2\left| \!{\underline {\,
  8,192 \,}} \right. \\
 & 2\left| \!{\underline {\,
  4,96 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2,48 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,24 \,}} \right. \\
\end{align}\]
The GCD is $2\times 2\times 2=8$ and the LCM is $2\times 2\times 2\times 24=192$.
Now we find that multiplication of those numbers and the multiplication of LCM and HCF, both give $8\times 192=1536$.
So, the correct answer is “Option B”.

Note: We need to remember that the LCM has to be only one number. It is the least common multiple of all the given numbers. If the given numbers are prime numbers, then the LCM of those numbers will always be the multiple of those numbers. These rules follow for both integers and fractions.