Question

How do you find the least common multiple of $24$ and $14$?

Answer 1

Hint: Here we will find the least common multiple of given numbers.
First address input parameters and values integers. Arrange a group of numbers in the horizontal form with space or comma separated format.
Choose the divisor which divides each or most of the integers in the group, divide each integer separately and write down the quotient in the next line right under the respective integers.
Bring down the integer to the next line if the integer is not divisible by the divisor. Repeat the same process until all the integers are brought to $1$.
Then multiply the divisors to find the LCM.

Complete step-by-step solution:
First address input parameters and values integers that is $24$ and $14$,
Arrange group of numbers in the horizontal form with space or comma separated format $14,24$
$\begin{array}{*{20}{c}}
  {2\left| \!{\underline {\,
  {14\,\,,\,\,24} \,}} \right. } \\
  {7\left| \!{\underline {\,
  {7\,\,\,,\,\,12} \,}} \right. } \\
  {12\left| \!{\underline {\,
  {1\,\,,\,12} \,}} \right. } \\
  {\,\,\,\,\,\underline {1\,\,,\,\,1} }
\end{array}$
Here we choose the first divisor is $2$ which divides the integers in the group, divide the each integers separately and we write down the quotient in the next line right under the respective integers.
And then choose the second divisor $7$ which divides the only one integer in the group so we divide that number and write the quotient in the next line and then keep the other integer in the group which is written in the next line.
Now choose the divisor for the remaining integer and divides that number then write the quotient in the next line. Finally we brought $1$. Now we are going to the next process that is multiply the divisors
$ \Rightarrow 2 \times 7 \times 12 = 168$

Hence least common multiple of $24$ and $14$ is $168$

Note: We can also find the LCM by using prime factorization.
That is the prime factorization of $14 = 2 \times 7$ and the prime factorization of $24 = 2 \times 2 \times 2 \times 3$ .
Multiply each factor the greater number of times it occurs that is LCM$ = 2 \times 2 \times 2 \times 3 \times 7$
We get LCM$ = 168$