Question

What is the least common multiple of \[2,9\,and\,6\]

Answer 1

Hint: In this question we have found the LCM of 2, 9 and 6. The LCM is the least common multiple and it is defined as \[LCM(a,b) = \dfrac{{\left| {a \cdot b} \right|}}{{\gcd (a,b)}}\] , where a, b and c are integers and \[\gcd \]is the greatest common divisor. We can find LCM by division method also. Here we solve by formula.

Complete step-by-step answer:
Consider the given numbers 2, 9 and 6.
First, we divide each by 2 if the number divides by 2 then we write the quotient otherwise we write the same number in the next line. Next, we will divide the numbers by 3 and the same procedure of writing is carried out. Again, next we divide by 3 and the same as above and hence we obtain 1 in the last row. This is the end of the division procedure. We have to divide till we get 1 in the next row.
\[
  2\,\left| \!{\underline {\,
  {2,\,9,\,6} \,}} \right. \\
  3\,\,\left| \!{\underline {\,
  {1,\,9,\,3} \,}} \right. \\
  3\,\,\left| \!{\underline {\,
  {1,\,3,\,1} \,}} \right. \\
  \,\,\,\,\,1,\,1,\,1 \\
 \]
Here we will consider the numbers by which we have divided the three numbers.
Now to find LCM of the given numbers we have to multiply the first column numbers that is
\[LCM = 2 \times 3 \times 3\]
\[ \Rightarrow LCM = 18\]
Therefore, the LCM of 2, 9 and 6 is 18.
If we have 3 numbers, we use the division method to find the LCM. Suppose if we want to find LCM of 2 numbers, we use the formula and hence we obtain the solution.
So, the correct answer is “18”.

Note: We must know about the multiplication, division and tables of multiplication to solve the question. We should divide by the number by the least number and hence it is the correct way to solve the problem.