Question

What is the least common multiple of 2, 6, and 8?

Answer 1

Hint: To find the value of the least common multiple of 2, 6, and 8, we will use the ladder method. In this method, we have to write the numbers whose LCM is to be found horizontally. In the left side, we will write the prime numbers that are used to factorize each of these numbers. We have to write the quotient of this division in the next row. We have to do this procedure till all the quotients become one.

Complete step-by-step solution:
We have to find the least common multiple (LCM) of 2, 6, and 8. Let us use the ladder method. In this method, we will write the numbers whose LCM is to be found horizontally. In the left side, we will write the prime numbers that are used to factorize each of these numbers. Let us first write 2 which are the factors of 2,6 and 8.
$2\left| \!{\underline {\,
  2,6,8 \,}} \right. $
We will write the quotient of this division in the next row. We have to do this procedure till all the quotient becomes one.
\[\begin{align}
  & 2\left| \!{\underline {\,
  2,6,8 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,3,4 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,3,2 \,}} \right. \\
 & 3\left| \!{\underline {\,
  1,3,1 \,}} \right. \\
 & \text{ }\text{ }\text{ }1,1,1 \\
\end{align}\]
Now, to find the LCM, we have to multiply these prime factors.
Therefore, the LCM of 2, 4, 6 $=2\times 2\times 2\times 3=24$.

Note: Students can also find the LCM by listing the multiples of 2, 4 and 6.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16,18, 20, 22, 24, …
Multiples of 6: 6, 12, 18, 24, ….
Multiples of 8: 8, 16, 24, 32, 40, 48,…
We can see that the common multiples are 24, 48,… .Of these, we have to take the least number. Here, the least number is 24. Hence, the LCM of 2, 6 and 8 is 24.