Question

What is the least common multiple of 8 and 14?

Answer 1

Hint: We need to find the least common multiple of 8 and 14. First we need to find the common multiples of 14 and 8 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 solution:
We need to find the LCM of 8 and 14. LCM stands for least common multiple.
We first find the multiples of 14 and 8.
The multiples of 14 are $14,28,42,56,70,84,98,112,.......$.
The multiples of 8 are $8,16,24,32,40,48,56,64,72,80,88,96,104,112,........$.
The common multiples of 14 and 8 are $56,112$. It will keep going on.
The least common multiple of 14 and 8 is 56.
We also can use the simultaneous factorisation to find the greatest common factor of 14 and 8.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 2\left| \!{\underline {\,
  8,14 \,}} \right. \\
 & 1\left| \!{\underline {\,
  4,7 \,}} \right. \\
\end{align}\]
The LCM is $2\times 4\times 7=56$.

Therefore, the least common multiple of 14 and 8 is 56.

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.