# Is this right? LCM of 9x^3y^2 and 15xy^4z

#### crappiefisher26

##### New member
it says find the least common multiple of the two expressions and simplify.

9x^3y^2 and 15xy^4z .

No example given. How do you do this?

#### letsgetaway

##### New member
Re: Is this right?

crappiefisher26 said:
it says find the least common multiple of the two expressions and simplify.

9x^3y^2 and 15xy^4z .

No example given how do you do this?
The formatting looks wrong. You are making 9x have an exponent of 3y which has an exponent of 2. And the same for 15. Are you trying to say 9x times 3y times 2?

#### jonboy

##### Full Member
I think crappie means this: $$\displaystyle \L \;9x^3y^2\,&\,15xy^4z$$

#### letsgetaway

##### New member
Oh ok. That definitely makes it readable now.

To help you with the question, what is the smallest number (not zero) that is a multiple of 9 and 15? Hint:

9: 9, 18, 27, 36, 45
15: 15, 30, 45

thanks

#### jonboy

##### Full Member
crappiefisher26 said:
You know there is more to this exercise than just finding the LCM of 9 and 15, right?

#### Mrspi

##### Senior Member
crappiefisher26 said:
it says find the least common multiple of the two expressions and simplify.

9x^3y^2 and 15xy^4z .

No example given. How do you do this?
9x^3 y^2 can be written as 3*3*x*x*x*y*y

15x y^4 z can be written as 3*5*x*y*y*y*y*z

The least common multiple of these numbers must contain ALL of the factors of the number, each to the Highest power that each factor appears.

Since 3 appears twice, we need 3^2.

Since 5 appears once, we need 5.

Since x appears three times as a factor (in 9 x^3 y^2), we need x^3

Since y appears 4 times as a factor (in 15 x y^4 z), we need y^4

Since z appears just once in (15 x y^4 z), we need z.

So, the least common multiple must contain these things: 3^2 * 5 * x^3 * y^4 * z

Or, 45 x^3 y^4 z

#### jonboy

##### Full Member
Wow that was a really good explanation Mrspi. 