finding the LCM...
10q2, 35s2t2
and
4x - 12, 2x - 6

- anonymous

finding the LCM...
10q2, 35s2t2
and
4x - 12, 2x - 6

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- anonymous

@jim_thompson5910

- jim_thompson5910

what is the LCM of 10 and 35

- anonymous

i don't know :(

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## More answers

- jim_thompson5910

list out the multiples of each and see what multiples they have in common

- anonymous

5

- jim_thompson5910

multiples of 10
10, 20, 30, ...
multiples of 35
35, 70, 105, ...

- anonymous

oh I'm a idiot. okay yes makes so much more sense then me over here. let me do that now.

- anonymous

70, 140, 210, 280.

- jim_thompson5910

which is the smallest common multiple

- anonymous

sorry jim. I'm a little slow. and its 70.

- jim_thompson5910

correct

- jim_thompson5910

now with the variable portion, we just multiply the distinct factors q^2, s^2, t^2
So the LCM is \(\Large 70q^2s^2t^2\)

- anonymous

i had that before and i thought it was wrong but okay good to know!

- anonymous

i had for the next one 4(x-3) is that wrong?

- jim_thompson5910

that's when you factor 4x - 12

- jim_thompson5910

how about the factorization of 2x - 6

- anonymous

when i do the multiple thing?

- anonymous

thats called factorization? dont want to be over here doing something way different then your asking me to do.

- jim_thompson5910

yeah when you go from 4x - 12 to 4(x-3). It's called factoring

- jim_thompson5910

you factor the terms as much as possible to help find the LCM

- jim_thompson5910

4x - 12 factors to 4(x-3)
2x - 6 factors to 2(x-3)

- anonymous

okay. that makes some sense.

- jim_thompson5910

what is the LCM of 4 and 2

- anonymous

8

- jim_thompson5910

there's a smaller common multiple: it's 4

- jim_thompson5910

4 is a multiple of itself

- anonymous

i was thinking that but wasn't sure if that counted because it as you said is a multiple of its self.

- jim_thompson5910

so the LCM of 4(x-3) and 2(x-3) is \(\Large 4(x-3)\)
we only list the (x-3) factor once because we list the highest unique factorization

- anonymous

okay, so thats it?

- jim_thompson5910

yes

- anonymous

thats what i had before. ill argue that its right if my teacher says its wrong again!! if i need you again ill reach out! thanks so much.. thanks for the patience too!

- jim_thompson5910

well you can either say 4(x-3) or 4x-12

- jim_thompson5910

either works

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