Least common multiple 9 7 6

[Ati]

Hello Everyone! I am trying to re-learn math from scratch and I have this issue finding the LCM of these 3 numbers; 9 7 6

Here's how I tried to do it ( was working before all the time) 9 = 3x3 7=7 6=2x3 = 3x3x7x2x3 which is 378

Looked it up and all I could find is just the end result which is; 2x3x3x7 = 126 Like what? one of the 3's just gone but why?
If someone could explain it would be awesome Thank You!

 

[Harry_the_cat]

Remember you are trying to find the LOWEST common multiple. You have found a common multiple but not the lowest one.

2 x 3 x 3 x 7 includes 2 x 3 (ie 6), 3 x 3 (ie 9) and 7. You don't need to include another 3.

 

[pka]

Hello Everyone! I am trying to re-learn math from scratch and I have this issue finding the LCM of these 3 numbers; 9 7 6
Here's how I tried to do it ( was working before all the time) 9 = 3x3 7=7 6=2x3 = 3x3x7x2x3 which is 378

You need to learn a very simple rule. To find the [imath]LCM[/imath] write each number in factored form.
In this case: [imath]9=3^2,~7=7~\&~6=2\cdot 3[/imath].
Then write down each prime factor [imath]2\cdot 3\cdot 7[/imath], next take highest power of each [imath]2^1\cdot 3^2\cdot 7^1=126[/imath]