I'm struggling with the following question:

let a, b, c, k, l be integers

Prove that if: a|b and a|c then a|(kb + lc)

I'm not looking for the answer outright just a little help.

I realise that:

b = ka

c = la

(kb + lc) = m x a

The approach I've been taking so far is to go: b + c = ka + kl and then try to rearrange (ka + kl) to (kb + lc) since I know that

if a|b and a|c then a|(b + c)

Am I on the right track? If so then I know it's my algebra skills which are the problem.