# What is the LCM of 5 and 9?

Jun 27, 2017

It is $45$. See explanation.

#### Explanation:

The lowest common multiple (LCM) of numbers $a$ and $b$ can be calculated as:

## $\lcm \left(a , b\right) = \frac{a \times b}{\gcd} \left(a , b\right)$

where $\gcd$ is the greatedt common divisor

In the given example the greatest common divisor (gcd) is $1$, so the lowest common multiple is $\lcm \left(5 , 9\right) = 5 \times 9 = 45$

Jun 27, 2017

$\text{LCM(5,9)=45}$

#### Explanation:

Multiples of $5 : \left\{5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , \textcolor{red}{45} , 50 , 55 , 60 , \ldots\right\}$

Multpiles of $9 : \left\{9 , 18 , 27 , 36 , \textcolor{red}{45} , 54 , 63 , 72 , \ldots .\right\}$

From the lists we see that 45 is the [least common multiple].(https://socratic.org/prealgebra/factors-and-multiples/least-common-multiple)

$\text{LCM(5,9)=45}$