1. ## Lcm

I just have one problem that is driving me nuts, and I'm hoping I'm not missing out on an important rule.

My book says the LCM of 48 and 54 is 432. I keep getting 288 though.

(* = "to the power of")
I factored 48 and got 2*3 times 3
I factored 54 and got 3*2 times 2.

So...unless I'm mistaken, according to the rules I multiply 2*3 times 3*2. I keep getting 288.

My apologies in advance if this is a simple computation error, but I just can't get it right.

2. Hello, endlesst0m!

You made a series of silly mistakes.
Don't kick yourself too hard . . .

My book says the LCM of 48 and 54 is 432.
I keep getting 288 though.

I factored 48 and got: .$\displaystyle 2^3\cdot3$ . . . . No

I factored 54 and got: .$\displaystyle 2\cdot3^2$ . . . . No

According to the rules, I multiply: .$\displaystyle 2^3\cdot 3^2 \:=\:288$ . . . . No
Let's start again . . .

. . $\displaystyle 48 \:=\:2^{\color{red}4}\cdot 3$

. . $\displaystyle 54 \:=\:2\cdot3^{\color{red}3}$

Therefore: .$\displaystyle \text{LCM} \:=\:2^4\cdot3^3 \:=\:432$

3. Now I'm stuck again. I just don't have the mind for math (not that I can't get a decent grade if I try). But anyway, here's my other LCM/GCF problem

I need to find the LCM and GCF of 40 and 900(* = "to the power of").

I determined that 40 factors to 2*3 times 5

And that 900 factors to 5*2 times 6*2

Therefore GCF: 5 times 5

LCM: 5*2 times 6*2 times 2*3

I'm getting the right answer for GCF but I'm not sure if I'm doing it right. I can't get the right answer for LCM however.

4. Hello, endlesst0m!

Find the LCM and GCF of 40 and 900.

I determined that: .$\displaystyle 40 \:=\:2^3\cdot 5$ . . . . Yes

And that: .$\displaystyle 900 \:=\:5^2\cdot6^2$ . . . . not completely factored!

Therefore: .$\displaystyle \text{GCF} \:=\:5\cdot 5$ . . . . what?

and: .$\displaystyle \text{LCM} \:=\:5^2\cdot6^2\cdot 2^3$ . . . . no

I'm getting the right answer for GCF. . . . . No, you're not!
I can't get the right answer for LCM however. . . . . No wonder!
Factor completely: . $\displaystyle 40 \:=\:2^3\cdot5\qquad900 \:=\:2^2\cdot3^2\cdot5^2$

. . $\displaystyle \text{GCF} \;=\;2^2\cdot5 \;=\;20$

. . $\displaystyle \text{LCM} \;=\;2^3\cdot3^2\cdot5^2 \;=\;1800$