Question

Find the LCM of 21x^2 + 105x and 3x^2 + 24x + 45

Answer 1

6x^2 + 30x can factor to 6x(x+5)
3x^2 + 18x + 15 can factor to (x+5)(3x+3)

so the least common multiple is (x+5)

Answer 2

@thechocoluver445 you have found the greatest common divisor (GCD). the LCM is different.

Answer 3

well 3x^2 + 18x + 15 = 3(x+1)(x+5)
so the lcm is 3. my bad.

Answer 4

This is still wrong I'm afraid.
@byndbtch if you want to learn about this there is a good explanation here: http://www.purplemath.com/modules/lcm_gcf.htm

Answer 5

oh, would the lcm be 3(x+5)? sorry, i have done this in a while..

Answer 6

you correctly found that:

6x^2 + 30x can factor to 6x(x+5) = 2 * 3 * x * (x+5)
3x^2 + 18x + 15 can factor to (x+5)(3x+3) = 3 * (x+5) * (x+1)

now if you compare the two, you need to find the product of all "unique" factors of both numbers.
in this case the LCM = 2*3*x*(x+5)*(x+1) = 6x(x+5)(x+1)

Answer 7

how about this one?? 35y^2 + 175y and 7y^2 + 42y + 35

Answer 8

Use the same principals - that link I gave above explains LCM in a lot of detail.

Answer 9

ty but it is not sinking in. I appreciate your help.

Answer 10

it might help if you at least try to solve it. just post the steps that you /think/ you need to take and I will guide you if necessary to the correct solution.

Answer 11

e.g. the first step is to factorise each polynomial

Answer 12

21y^2 + 84y = 21y(y +21)

Answer 13

thats not right

Answer 14

its /almost/ right, HINT: 84 = 21 * 4

Answer 15

21y(y + 4) ??

Answer 16

perfect!
now factorise the other polynomial as well please

Answer 17

21y(y +4)(y +1)

Answer 18

BTW: What are the two polynomials you are working with here?

Answer 19

I'm asking because I noticed that you have changed the original polynomials that you posted in this question.

Answer 20

21y^2 + 84y and then 7y^2 + 42y +56

Answer 21

ok, so you factorised the first one correctly:
21y^2 + 84y = 21y(y + 4)

but the second factorisation does not look correct for 7y^2 + 42y +56

Answer 22

do you want to try again with that one?

Answer 23

yeah sorry about that, i was rushing and kept confusing gcf with lcf with lcm...sorry :/

Answer 24

@thechocoluver445 np :)

Answer 25

acco\rding to my question, the answer is 21y(y+4)(y +2) which I have no idea where the 2 came from????

Answer 26

ignore the answer for now.
lets look at the second polynomial which is: 7y^2 + 42y +56
notice all the terms can be divided by 7

Answer 27

right

Answer 28

so 7y^2 + 42y +56 = 7(y^2+6y+8)
can you factorise y^2+6y+8?

Answer 29

not really....as I do notunderstand where the 6and 8 came from

Answer 30

7*6 = 42
7*8 = 56

so: 7(y^2+6y+8) = 7y^2 + (7*6)y + (7*8) = 7y^2 + 42y + 56

Answer 31

does it make any sense now?

Answer 32

no it really doesnt but I do appreciate the effort....Im going to take a break now....thanks again.

Answer 33

np - let me know if you need more help at a later date and I'll be more than happy to help :)