# How do you find the Least common multiple of 30, 25, 10?

Mar 10, 2018

Least common multiple of $30 , 25$ and $10$ is $150$

#### Explanation:

To find the least common multiple of numbers, we should first find out their prime factors. Here we have three numbers $30 , 25$ and $10$ and their prime factors are as given below.

$30 = 2 \times \textcolor{b l u e}{3} \times \textcolor{red}{5} = {2}^{1} \times {3}^{1} \times {5}^{1}$
- Observe that each of $2 , 3$ and $5$ appear just once.

$25 = \textcolor{red}{5 \times 5} = {5}^{2}$
- Observe that only $5$ appears and it appears twice.

$10 = 2 \times \textcolor{red}{5} = = {2}^{1} \times {5}^{1}$
- Observe that $2$ and $5$ appear but once only.

While to find least common multiple of numbers, we take all common factors and raise them to the highest power relating to them. Here, while highest power of $2$ is $1$, that of $3$ is $1$ and that of $5$ is $2$ .

Hence least common multiple of $30 , 25$ and $10$ is ${2}^{1} \times {5}^{2} \times {3}^{1} = 2 \times 3 \times 5 \times 5 = 150$

Note $-$ For GCF, pick up least number of times. Here least power of $2$ is $0$, that of $3$ is $0$ and that of $5$ is $1$, hence GCF is $5$.