To find the Least Common Denominator (LCD) for the equation \( \frac{3}{5x} - \frac{3}{2x} = 10 \), we first list the denominators present in the fractions, which are \( 5x \) and \( 2x \).
- The denominators are \( 5x \) and \( 2x \).
- We first find the least common multiple (LCM) of the numerical parts, which are \( 5 \) and \( 2 \).
- The LCM of \( 5 \) and \( 2 \) is \( 10 \).
- The variable part is \( x \) (which is common in both denominators).
Now, we can combine these to get the LCD:
- The LCD = \( 10x \)
Thus, the Least Common Denominator (LCD) for the equation \( \frac{3}{5x} - \frac{3}{2x} = 10 \) is \( \boxed{10x} \).