finding the LCM...

10q2, 35s2t2

and

4x - 12, 2x - 6

Question

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

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

what is the LCM of 10 and 35

anonymous · Answer

i don't know :(

jim_thompson5910 · Answer

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

anonymous · Answer

5

jim_thompson5910 · Answer

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

anonymous · Answer

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

anonymous · Answer

70, 140, 210, 280.

jim_thompson5910 · Answer

which is the smallest common multiple

anonymous · Answer

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

jim_thompson5910 · Answer

correct

jim_thompson5910 · Answer

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 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

that's when you factor 4x - 12

jim_thompson5910 · Answer

how about the factorization of 2x - 6

anonymous · Answer

when i do the multiple thing?

anonymous · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

okay. that makes some sense.

jim_thompson5910 · Answer

what is the LCM of 4 and 2

anonymous · Answer

8

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

4 is a multiple of itself

anonymous · Answer

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

jim_thompson5910 · Answer

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 · Answer

okay, so thats it?

jim_thompson5910 · Answer

yes

anonymous · Answer

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 · Answer

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

jim_thompson5910 · Answer

either works