In equality
$$1 * 2 * 3 * 4 * 5 * ... * 60 * 61 * 62 = 2023$$
Instead of each asterisk, you need to put one of the signs “+” (plus), “-” (minus), “•” (multiply) so that the equality becomes true. What is the smallest number of "•" characters that can be used?
1. **Initial Consideration**:
   - We need to find the smallest number of multiplication signs (denoted as "•") to make the equation \(1 * 2 * 3 * 4 * 5 * \ldots * 60 * 61 * 62 = 2023\) true.
   - If we use only addition and subtraction, the maximum sum is \(1 + 2 + 3 + \ldots + 62\), which is less than 2023.

2. **Sum Calculation**:
   - Calculate the sum \(S\) of the first 62 natural numbers:
     \[
     S = \frac{62 \cdot (62 + 1)}{2} = \frac{62 \cdot 63}{2} = 1953
     \]
   - Since \(1953 < 2023\), we need at least one multiplication to increase the total.

3. **Parity Consideration**:
   - The sum \(S = 1953\) is odd.
   - If we place one multiplication sign between \(a\) and \(a+1\), the result will be:
     \[
     S - a - (a+1) + a(a+1) = 1953 - a - (a+1) + a(a+1)
     \]
   - This expression simplifies to:
     \[
     1953 - a - a - 1 + a^2 + a = 1953 - 1 + a^2 - a = 1952 + a^2 - a
     \]
   - Since \(a^2 - a\) is always even, the result \(1952 + a^2 - a\) is even. Therefore, it cannot be 2023, which is odd.

4. **Using Two Multiplications**:
   - We need to find a way to use two multiplications to achieve the target sum of 2023.
   - Consider placing multiplications between \(1\) and \(2\), and between \(9\) and \(10\):
     \[
     1 \cdot 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 \cdot 10 + 11 + \ldots + 62
     \]
   - Calculate the new sum:
     \[
     1 \cdot 2 = 2
     \]
     \[
     9 \cdot 10 = 90
     \]
     \[
     \text{Sum of remaining terms} = 3 + 4 + 5 + 6 + 7 + 8 + 11 + 12 + \ldots + 62
     \]
   - Calculate the sum of the remaining terms:
     \[
     \text{Sum of } 3 \text{ to } 8 = 3 + 4 + 5 + 6 + 7 + 8 = 33
     \]
     \[
     \text{Sum of } 11 \text{ to } 62 = \frac{(62 - 11 + 1) \cdot (11 + 62)}{2} = \frac{52 \cdot 73}{2} = 1898
     \]
   - Adding all parts together:
     \[
     2 + 90 + 33 + 1898 = 2023
     \]

Thus, the smallest number of multiplication signs needed is 2.

The final answer is \(\boxed{2}\).