To find the least common denominator (LCD) for the fractions $\frac{1}{3}$ and $\frac{1}{4}$, we need to determine the least common multiple (LCM) of the denominators 3 and 4.

Steps:

1. The denominators are 3 and 4.
2. The multiples of 3 are: 3, 6, 9, 12, 15, 18, etc.
3. The multiples of 4 are: 4, 8, 12, 16, 20, etc.
4. The smallest number that appears in both lists of multiples is 12.

Thus, the least common denominator (LCD) is 12.

Would you like further details or have any questions? Here are five related questions:

1. How would you convert $\frac{1}{3}$ and $\frac{1}{4}$ to have a denominator of 12?
2. How do you find the least common multiple (LCM) for more than two numbers?
3. What happens when you add or subtract fractions with different denominators?
4. How can we simplify a fraction after finding the LCD?
5. What are the steps for finding the greatest common divisor (GCD)?

Tip: When finding the LCD, listing the multiples of each denominator can help you quickly spot the smallest common multiple.