Finding the Lowest Common Multiple Question

[Plasma]

Hey guys,

I've always been so horrible at math. It just doesn't stick for me. Teachers always go too fast or to slow, or change the methods and I never get to understand. Anyway here is my question:

So, i've got to Find the LCD by LCM of 12 and 16

So,

12 = 2 x 2 x 3

16 = 2 x 2 x 2 x 2


Here is what I don't understand,

From the corrections my teacher made, the number i'm supposed to get is 48. Obviously to get 48, it's " 2 x 2 x 2 x 2 x 3 " ( 2^4 x 3)


WHY ISN'T IT:

" 2 x 2 x 2 x 2 x 2 x 2 x 3 " (2^6 x 3)

Where and how did one set of 2 x 2 get cancelled out? This is what I don't understand. If anyone could please clarify I would greatly appreciate it.




The method of finding the LCD my teacher is using isn't the factor tree method, it's this which I don't understand whatsoever:

 

[DrSteve]

For each prime number you take the highest number of times that prime appears in each factorization.

So 2 appears 2 times in 12, and 4 times in 16. Thus you take four 2's.
Also 3 appears 1 time in 12, and 0 times in 16. Thus you take one 3.

So the lcm is (2)(2)(2)(2)(3)=48.

What you did was take all factors that appear anywhere. This gives you the product of the two numbers, not the lcm. That is, you just multiplied the two numbers together.

 

[Plasma]

For each prime number you take the highest number of times that prime appears in each factorization.

So 2 appears 2 times in 12, and 4 times in 16. Thus you take four 2's.
Also 3 appears 1 time in 12, and 0 times in 16. Thus you take one 3.

So the lcm is (2)(2)(2)(2)(3)=48.

What you did was take all factors that appear anywhere. This gives you the product of the two numbers, not the lcm. That is, you just multiplied the two numbers together.

Ahhh, thank you so much for the clarification, greatly appreciated.

 

[lookagain]

Hey guys,

I've always been so horrible at math. It just doesn't stick for me. Teachers always go too fast or to slow, or change the methods and I never get to understand. Anyway here is my question:

So, i've got to Find the LCD by LCM of 12 and 16

Plasma,

also, the least common mutliple of two integers is their product divided
by their greatest common factor.

Here, the product is 12(16) = 192.

The greatest common factor is 4.

So, the least common >> multiple << is 192/4 = 48.


Edit ^^^

 

[mmm4444bot]

I've always been so horrible at math. It just doesn't stick for me.

You might not be doing enough homework.

Math was very hard for me, when I started. I forced myself to do two or three times as many exercises as assigned, if needed, until I was confident that I understood the material.