Question

Prove the following:
If a is divisible by 3 and b is divisible by 4 then a × b is divisible by 6.

Answer 1

Hey :)

Answer 2

So if a is divisible by 3,
it means that a is equal to some integer multiple of 3s.
\(\large\rm a=3k,\qquad k\in\mathbb Z\)

Answer 3

We can do similarly with b, it's some amount of 4s,
\(\large\rm b=4\ell,\qquad \ell\in\mathbb Z\)

Answer 4

So then our product,\[\large\rm ab\quad=\quad (3k)(4\ell)\quad=\quad 12k\ell\]Hmm do you see the next step? :)

Answer 5

yes, thank you!
12kl is divisible by 6

Answer 6

Good!
\(\large\rm =6(2k\ell)\)

Since k and l are integers, 2kl is an integer as well,
so it works out!

Yay team! ୧ʕ•̀ᴥ•́ʔ୨

Answer 7

thank you very much :)