Question

Find L.C.M of $9,18,36$.

Answer 1

Hint: We need to find the least common multiple of 9, 18 and 36. First we need to find the common multiples of 9, 18 and 36 from their multiples. Then we find the least common one among them. We can also take the simultaneous factorisation of those two numbers to find the LCM.

Complete step-by-step answer:
We need to find the LCM of 9, 18 and 36. LCM stands for least common multiple.
We first find the multiples of 9, 18 and 36.
The multiples of 9 are $9,18,27,36,45,54,63,72,.......$.
The multiples of 18 are $18,36,54,72,.......$.
The multiples of 36 are $36,72,108,.......$.
The common multiples of 9, 18 and 36 are $36,72$. It will keep going on.
The least common multiple of 9, 18 and 36 is 36.
We also can use the simultaneous factorisation to find the greatest common factor of 9,18 and 36.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 3\left| \!{\underline {\,
  9,18,36 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3,6,12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,2,4 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,1,2 \,}} \right. \\
\end{align}\]
The LCM is $3\times 3\times 2\times 2=36$.
Therefore, the least common multiple of 9, 18 and 36 is 36.
So, the correct answer is “36”.

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.