Question

Find the LCM of the given numbers by division method for 6, 8, 45.

Answer 1

Hint: We need to find the least common multiple of 6, 8 and 45. We will take the simultaneous factorisation of those three numbers to find the LCM.

Complete step-by-step answer:
We need to find the LCM of 6, 8 and 45. LCM stands for least common multiple.
We first find the multiples of 6, 8 and 45.
We use the simultaneous factorisation to find the greatest common factor of 6,8 and 45.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 2\left| \!{\underline {\,
  6,8,45 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3,4,45 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,4,15 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,2,15 \,}} \right. \\
 & 3\left| \!{\underline {\,
  1,1,15 \,}} \right. \\
 & 5\left| \!{\underline {\,
  1,1,5 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,1,1 \,}} \right. \\
\end{align}\]
The LCM is $2\times 3\times 2\times 2\times 3\times 5=360$.
Therefore, the least common multiple of 6, 8 and 45 is 360.
So, the correct answer is “360”.

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.