3. (3 points) The greatest common divisor of two numbers is 20, and the least common multiple is 100. The number of correct statements below is ( ).
(1) The product of the two numbers is 2000.
(2) If both numbers are multiplied by 10, the greatest common divisor increases by 100 times.
(3) If both numbers are multiplied by 10, the least common multiple increases by 10 times.
(4) If both numbers are multiplied by 10, the product of the two numbers increases by 100 times.
A. 1
B. 2
C. 3
D. 4
【Analysis】According to "the greatest common divisor of two numbers is 20, and the least common multiple is 100", it can be known that these two numbers are 20 and 100, and the solution can be obtained by analyzing each item accordingly.

【Solution】According to the problem, it is known that these two numbers are 20 and 100;
(1) $20 \times 100=2000$, so the product of the two numbers is 2000, so the original statement is correct;
(2) If both numbers are multiplied by 10, the greatest common divisor becomes $20 \times 10=200$, which is 10 times larger, so the original statement is incorrect;
(3) If both numbers are multiplied by 10, the least common multiple becomes $100 \times 10=1000$, which is 10 times larger, so the original statement is correct;
(4) If both numbers are multiplied by 10, they become 200 and 1000, and the product becomes 200000, which means the product of the two numbers is 100 times larger, so the original statement is correct;

There are 3 correct statements.
Therefore, the answer is: $C$.