5. (5 points) It is known that natural numbers $a, b$ satisfy two conditions:

- the sum of $a$ and $b$ is 546,
- the least common multiple of $a$ and $b$ is 22 times their greatest common divisor.

Find $a$ and $b$.
5. 462 and 84, or 84 and 462.

$+(5$ points) - the solution is correct.

+- (3 points) - the solution is generally correct, but not all cases for numbers $a$ and $b$ are considered.

-+ (2 points) - in the solution, the correct conclusion is drawn from the relation $\frac{[a, b]}{(a, b)}=22$ about the canonical decomposition of numbers $a$ and $b$, but the solution did not proceed further.