Question

What is the least common multiple of 4,6 and 9?

Answer 1

Hint: We know that the multiples are the product of a given number with an integer. First we will find the multiples of 4, 6 and 9 individually and compare the multiples to find the least common multiple.

Complete step by step answer:
We have been given numbers 4, 6 and 9.
We have to find the least common multiple of 4, 6 and 9.
Now, we know that Multiples are the product of a given number with an integer.
First we will obtain the multiples of 4 by multiplying the 4 by another whole number. Then we will get
Multiples of 4 $\Rightarrow 4=\left\{ 4,8,12,16,20,24,28,32,36....... \right\}$
Now, let us obtain the multiples of 6 by multiplying the 6 by another whole number. Then we will get
Multiples of 6 $\Rightarrow 6=\left\{ 6,12,18,24,30,36....... \right\}$
Now, let us obtain the multiples of 9 by multiplying the 9 by another whole number. Then we will get
Multiples of 9 $\Rightarrow 9=\left\{ 9,18,27,36....... \right\}$
Now, we know that the multiple of any number must be greater than or equal to that number.
Now, we will find that the least common multiple of 4, 6 and 9, then we will get
$\Rightarrow \left\{ 36 \right\}$

Hence we get the least common multiple of 4, 6 and 9 as 36.

Note: Alternatively we can use the prime factorization method to find the least common multiple also known as LCM. We can find the LCM of all three numbers. Factors of a number are those numbers which divide the given number completely without leaving the remainder.