Proof Accuracy Check

[toughcookie723]

I would really appreciate it if someone could take a look at this and tell me if it is a correct proof!

If 4|x and 6|x then 12|x.

4|x ==> x = 4a for some a
6|x ==> x=6b for some b
4a = 6b
4a = 6b ==> 2a = 3b which implies 2|b ==> b = 2c for some c
But x = 6b = 6(2c) = 12c ==> 12|x

Thank you!!!

 

[pka]

I would really appreciate it if someone could take a look at this and tell me if it is a correct proof!
If 4|x and 6|x then 12|x.
4|x ==> x = 4a for some a
6|x ==> x=6b for some b
4a = 6b
4a = 6b ==> 2a = 3b which implies 2|b ==> b = 2c for some c
But x = 6b = 6(2c) = 12c ==> 12|x

That works.

Note \(\displaystyle \text{lcm}(4,6) = 12~.\)