There is a class of numbers, they are both multiples of 7 and 5, and when 9 is added, they become prime numbers. The smallest number in this class is
【Analysis and Solution】
Number Theory, Least Common Multiple, Prime Numbers.
A number that is a multiple of both 7 and 5 is a multiple of $[5,7]=35$;
$35 \times 0+9=9$ is not a prime number;
$35 \times 1+9=44$ is not a prime number;
$35 \times 2+9=79$ is a prime number;
The smallest number of this type is $35 \times 2=70$.