I4.1 Mr. Lee is $a$ years old, $a<100$.
I4.2 Mr. Lee has $a+b$ sweets. If he divides them equally among 10 persons, 5 sweets will be remained. If he divides them equally among 7 persons, 3 more sweets are needed. Find the minimum value of $b$.
If the product of $a$ and his month of birth is 253 , find the value of $a$.
$$
253=11 \times 23
$$
$11=$ his month of birth and $a=23$
$$
\begin{array}{l}
10 m+5=7 n-3=23+b \\
7 n-10 m=8
\end{array}
$$

By trial and error $n=4, m=2$
$$
\begin{array}{l}
23+b=7 \times 4-3=25 \\
b=2
\end{array}
$$