Question

What is the least common multiple of 6 and 9?

Answer 1

Hint: We need to find out the least common multiple of 6 and 9. We start to solve the problem by writing the multiples of the numbers 6 and 9. Then, we find the smallest common multiple of both the numbers.

Complete step by step answer:
We need to find the least common multiple of the numbers 6 and 9. We will be solving the given question by writing the multiples of both the numbers and then finding out the smallest common multiple of the numbers.
A multiple is a number that can be divided by another number several times without any remainder.
For example, we have the first five multiples of 8 as 8, 16, 24, 32, 40 .
It is because the product of each of the pairs (8,1) ,(8,2),(8,3),(8,4),(8,5) results in 8 , 16 , 24 , 32 , 40 respectively . Hence 8 , 16 , 24 , 32 , 40 are multiples of 8.
According to our question, we need to find out the multiples of 6 and 9.
Writing the first five multiples of 6, we have
$\Rightarrow 6\times 1=6$
$\Rightarrow 6\times 2=12$
$\Rightarrow 6\times 3=18$
$\Rightarrow 6\times 4=24$
$\Rightarrow 6\times 5=30$
The first five multiples of 6 are 6, 12, 18, 24, 30.
Writing the first five multiples of 9, we have
$\Rightarrow 9\times 1=9$
$\Rightarrow 9\times 2=18$
$\Rightarrow 9\times 3=27$
$\Rightarrow 9\times 4=36$
$\Rightarrow 9\times 5=45$
The first five multiples of 9 are 9, 18, 27, 36, 45.
Now, we have to find the least common multiple of 6 and 9.
From the above, we find that there is no number lesser than 18 that is a multiple of both 6 and 9. So, 18 is the smallest common multiple of 6 and 9.

$\therefore$ The least common multiple of 6 and 9 is 18.

Note: The result of the given question is correct if it divides both 6 and 9 exactly with no remainder.. In our question, we got the result of 18.
$\Rightarrow 6\times 3=18$
$\Rightarrow 9\times 2=18$
The number 18 divides 6 and 9 exactly with no remainder. The result attained is correct. The multiple is the result we get upon the multiplication of a number with the whole number.