Question

How do you find the least common multiple of $15,6?$

Answer 1

Hint:
For solving such types of questions you have to follow some steps. First find factors of $15$. After that find factors of $6$. And lastly multiply each factor the greater number of times it occurs in factors of $15$ and factors of $6$.

Complete step by step solution:
For finding Least Common Multiple of $15,6$ we follow below given steps.
First we will find factors of $15$.
For that we will factorize $15$
So, after that factors of $15$ is $1,3,5,15$
Here, for finding Least Common factor we need prime factors of $15$
So prime factors of $15$ is $3,5$
Now, we will find factors of $6$.
So, factors of $6$is $1,2,3,6$
For finding Least Common factor we need prime factors of $15$
So prime factors of $6$ is $2,3$
Now, Least Common factor of $15$ and $6$ is $2 \times 3 \times 5 = 30$

Here, $3$ is both prime factors so we only take one time.

Note:
Another method:
List of Multiples of $6$ is $\{ 6,12,18,24,30,....\} $
List of Multiples of $15$ is $\{ 15,30,45,.....\} $
Now, List of common multiples of $15$ and $6$ is $\{ 30,60,...\} $
So, Least common multiple of $15$ and $6$ is $30$