Question

How to find the LCM of the below ones.....

Answer 1

\[a ^{2}, a ^{2}+3a\]

Answer 2

You can get a common multiple, but not the LCM, by multiplying the 2 expressions together, just like you can get a multiple of 8 and 4 by multiplying, but it's not the LCM.

For this one, you can factor both expressions: a^2 = (a)(a) and a^2 + 3a = a(a+3)

Then cancel factors to both expressions... then the LCM will be the product of the unique factors

Answer 3

sorry, that last sentence should have read:

Then cancel factors COMMON to both expressions... then the LCM will be the product of the REMAINING unique factors

Answer 4

Will it be a(a+3)

Answer 5

Just a sec... checking to make sure I didn't make a dumb error...

Answer 6

I messed it up:

Imagine if a = 2.... then a^2 is 4 and a^2 + 3a = 10. LCM of 4 and 10 is 20...

factor 4 as (2)(2) and factor 10 as (2)(5) (in other words, (2)(2+3)) and then cancel ONE of the (2) factors.... not both.

leaving (2) and (2)(5) multiplying to make 20
OR
leaving (2)(2) and (5) also multiplying to make 20

Answer 7

You don't cancel the common factors from both terms, just from one or the other.

Answer 8

so a^2 -->> (a)(a)
and a^2 + 3a --->> a(a+3)

Cancel a single (a), then multiplying the remaining expressions to get a^2(a+3)

Answer 9

Ok thanks a lot!
I was a little bit confused about this...
Anyway i got it .
Thanks.. :)

Answer 10

Good :) I confused myself at first... it didn't seem right (and it wasn't), so I tried it with real numbers to be sure of the concept, then extended it back to the case with the variable.