# What's the Lowest Common Multiple (LCM) of 12 and 15?

##### 4 Answers

$L C M = 60$

#### Explanation:

When we're looking at the LCM (Least Common Multiple), we're looking for a number that both 12 and 15 are a factor of. Oftentimes people simply assume that if we multiply the two together, we'll find it. In this case, it'd be $12 \times 15 = 180$. 180 is a multiple of both, but is it the least one? Let's look.

I start with a prime factorization of both numbers:

$12 = 2 \times 2 \times 3$

$15 = 3 \times 5$

To find the LCM, we want to have all the prime factors from both numbers accounted for.

For instance, there are two 2s (in the 12). Let's put those in:

$L C M = 2 \times 2 \times \ldots$

There is one 3 in both the 12 and the 15, so we need one 3:

$L C M = 2 \times 2 \times 3 \times \ldots$

And there is one 5 (in the 15) so let's put that in:

$L C M = 2 \times 2 \times 3 \times 5 = 60$

$12 \times 5 = 60$
$15 \times 3 = 60$

Jan 30, 2018

$60$

#### Explanation:

another approach is to use teh relation

$a b = h c f \left(a , b\right) \lcm \left(a b\right)$

now $h c f \left(12 , 15\right) = 3$

$\therefore 12 \times 15 = 3 \times \lcm \left(12 , 15\right)$

$\lcm \left(12 , 15\right) = \frac{{\cancel{12}}^{4} \times 15}{\cancel{3}}$

$\lcm = 4 \times 15 = 60$

Feb 1, 2018

The LCM is $60$.

#### Explanation:

The LCM is the least common multiple. We can find the LCM by listing the multiples of the two numbers and identifying the lowest multiple they have in common.

$12 :$$12 , 24 , 36 , 48 , \textcolor{red}{60} , 72 , 84. . .$

$15 :$$15 , 30 , 45 , \textcolor{red}{60.} . .$

The LCM is $60$.

Feb 1, 2018

$60$

#### Explanation:

Let's try to find the LCM of $12$ and $15$.

We get:
$12 = 2 \cdot 2 \cdot \textcolor{b l u e}{3}$
$15 = \textcolor{b l u e}{3} \cdot 5$

We see that they both share $3$ is their LCM.

We divide each number by their LCM.

$\frac{12}{3} \implies 4$

$\frac{15}{3} \implies 5$

We multiply these two quotients and the LCM to get our final answer:

$3 \cdot 4 \cdot 5 = 60$

That is our answer!