7.2. Lada and Lera each thought of a natural number. If Lada's number is decreased by $5 \%$, and Lera's number is increased by $5 \%$, the results will be equal. It turned out that the numbers they thought of are the smallest with this property. What numbers did the girls think of?
Answer: 21 and 19.

Solution: Let Lada have guessed the number $a$, and Lera the number $b$. Then the new numbers $0.95 a$ and $1.05 b$ are equal, that is, $0.95 a = 1.05 b$. Simplifying this equation, we get $19 a = 21 b$. The left side is divisible by 19, so the right side must also be divisible by 19. Since 21 and 19 are coprime, $b = 19 k$, from which $a = 21 k$. Among all such numbers, the smallest are 21 and 19 when $k=1$.

Criteria: Only the answer, the answer with verification - 1 point. If it is not explained why $b$ must be divisible by 19 and $a$ by 21 - deduct 1 point.