Question

What is the least common multiple of 2,5,6 and 9?

Answer 1

Hint: The LCM or the least common multiple of a group of numbers can be found by listing the individual multiples of each of the given numbers and then finding the multiple which is common to all the numbers and which is the least in value among the other common multiples.

Complete step by step solution:
In the question we are given the numbers, 2,5,6 and 9. First let us write down all the multiples for each of the numbers. First, taking 4 and writing down its multiples, we get,
$\begin{align}
  & 2\times 1=2 \\
 & 2\times 2=4 \\
 & 2\times 3=6 \\
 & 2\times 4=8 \\
\end{align}$
And so on…. Hence, the multiples of 2 are 2,4,6,8,10….90
Next, find the multiples of 5, we get,
$\begin{align}
  & 5\times 1=5 \\
 & 5\times 2=10 \\
 & 5\times 3=15 \\
\end{align}$
And so on…. Hence, the multiples of 5 are 5,10,15,20,25….90
Next, find the multiples of 6, we get,
$\begin{align}
  & 6\times 1=6 \\
 & 6\times 2=12 \\
 & 6\times 3=18 \\
\end{align}$
And so on…. Hence, the multiples of 6 are 6,12,18,24,30….90
Next, find the multiples of 9, we get,
$\begin{align}
  & 9\times 1=9 \\
 & 9\times 2=18 \\
 & 9\times 3=27 \\
\end{align}$
And so on…. Hence, the multiples of 9 are 9,18,27,36….90

Finally, we can write down the common multiples among the given 4 members. Clearly, the least common multiple is 90. Hence the LCM or the least common multiple is the least valued common multiple which is 90.

Note: Another simple way to solve this type of problem is to check if the largest number given is a multiple of the other numbers, if this is true then we can conclude that the largest number is the LCM for the given group of numbers. But since 9 is not a multiple of 2,5, and 6 we cannot conclude that 9 is the LCM.