question multipliers

I've got a problem that asks: what multipliers can be used to eliminate fractions in the following equation?
t/3 + t/2 - 350 = 270

Two examples are given to me in the book, and when they use 2 as a multiplier, they get this equation :

5 (t - 420)/3 = 540

but I get: 5 (t - 700)/3 = 540 when I multiply everything by 2.


The other example they show in the book uses 3 as a multiplier, again they get:

5 (t - 420)/3 =810

but I get: 5 (t - 1050)/3 =810

How are they getting the number 420 in there no matter what they use as a multiplier? What am I doing wrong? ( I'm not trying to eliminate the fractions at this point, I'm just trying to figure out the method ! )
thanks in advance !

Well, I can explain the
5 (t - 420)/3 = 540
but not why they are doing it.
t/3 + t/2 - 350 = 270
Times 2
2t/3+t-700=540
5t/3-700=540
5t/3-2100/3=540
(5t-2100)/3=540
(5t-5*420)/3=540
5(t-420)/3 = 540

I don't know why it isn't
t/3 + t/2 - 350 = 270
t/3 + t/2 = 620
times 6
2t+3t=3720
5t=3720

Yes that helped

I understand what I did wrong now thanks to your explanation ! Thanks Gene. I posted this on another website and the help was not nearly as clear as your help was.

Darla