Question

What is the LCM of 9 and 12?
A) 3
B) 9
C) 18
D) 36

Answer 1

Have you tried using any formulas to solve this problem?

Answer 2

no but i think it may be B or C

Answer 3

Hmm... well lets talk about it first, we'll get to the bottom of it. Did you know that you can find the LCM of 2 numbers a and b by multiplying them together, then dividing by thir greatest common denominator (GCD)? You can also you a technique called prime factorization which is useful for finding the LCM of many numbers.

Answer 4

Let's use the first method.

\[LCM = \frac{ ab }{ GCD(a,b) }\]

Answer 5

ohhh i didnt know

Answer 6

mhmm

Answer 7

if we let a= 9 and b = 12, what is GCD(a,b)?

Answer 8

I think D.

Answer 9

Because 9, 18, 27, (36), 45 and for 12 its 12, 24 (36), 48

Answer 10

um either 21 or..somethingelse NO NOT 21 CUZ its not an option

Answer 11

but maybe 36??

Answer 12

Yes

Answer 13

@mrm is that right?

Answer 14

ITS 36
BECAUSE 9*4=36
AND
12*3=36

Answer 15

I just said that -_-

Answer 16

thankyou so much everyone yall are AMAZING PEOPLE or robots....but yeah thanks!!

Answer 17

another way is to take the prime factors

9 = 3 * 3
12 = 3 * 4

to get LCM use any common factors only once


so here LCM = 3 * 3 * 4 = 36

Answer 18

The GCD is the greatest common denominator, also known as the greatest common factor GCF.
If we look at 9 we see that it is divisible by 1,3, and 9.
If we look at 12 we see it is divisible by 1,2,3,4,6, and 12.
So we see our GCD is 3.

36 is right but I want you to know why it's right.

Answer 19

ohhh i see.

Answer 20

So by our formula...

\[LCM = \frac{ ab }{ GCD(a,b) } = \frac{ (9)(12) }{ GCD(9,12) } = \frac{ 108 }{ 3 } = 36\]

Answer 21

This always works for any two numbers.

Answer 22

that makes a lot more since now thanks!

Answer 23

i just did not know at 1st

Answer 24

That's what learning is all about!

Answer 25

Thanks again than,ill fan u in a min