Not knowing the $\mathrm{gcd}$ and $\mathrm{lcm}$ and knowing $\mathrm{gcd+lcm}$, how to find $a$ and $b$ in $\mathrm{gcd}(a,b)$?

Question

Here's what we have:

$\mathrm{gcd}(a,b)=d$ ; $\mathrm{lcm}(a,b)=m$ ; $a+b=30$ ; $m+d=42$ ; $b>a$.

What I tried:

if $d$ divides $a$ and $b$ so it divides $a+b$ so $d$ divides $30$. And with $\mathrm{gcd}$ and $\mathrm{lcm}$ rules I found that $md=ab$. But that's all, I didn't know how to continue.

Thanks.

Answer 1

Hint: This might help narrowing down the search: $d$ also divides $m$ (and hence it divides $42$).