Question

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

Answer 1

`LCM=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 `12xx15=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=2xx2xx3`

`15=3xx5`

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:

`LCM=2xx2xx...`

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

`LCM=2xx2xx3xx...`

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

`LCM=2xx2xx3xx5=60`

`12xx5=60`
`15xx3=60`

Answer 2

`60`

Explanation:

another approach is to use teh relation

`ab=hcf(a,b)lcm(ab)`

now `hcf(12,15)=3`

`:.12xx15=3xxlcm(12,15)`

`lcm(12,15)=(cancel(12)^4xx15)/cancel(3)`

`lcm=4xx15=60`

Answer 3

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,color(red)60,72,84...`

`15:` `15,30,45,color(red)60...`

The LCM is `60`.

Answer 4

`60`

Explanation:

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

We get:
`12=2*2*color(blue)3`
`15= color(blue)3*5`

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

We divide each number by their LCM.

`12/3=>4`

`15/3=>5`

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

`3*4*5=60`

That is our answer!