Tia visits her grandmother every \( 4^{\text {th }} \) day. Her twin brother Jay visits every \( 3^{\text {rd }} \) day. What is the first day when their visits will coincide?

To find the first day when Tia's and Jay's visits will coincide, we need to determine the least common multiple (LCM) of the two visit intervals: Tia visits every 4 days and Jay visits every 3 days. 1. **Identify the visit intervals:** - Tia's interval: \( a = 4 \) - Jay's interval: \( b = 3 \) 2. **Calculate the LCM of \( a \) and \( b \):** The LCM can be calculated using the formula: \[ \text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)} \] where GCD is the greatest common divisor. 3. **Find the GCD of 4 and 3:** Since 4 and 3 have no common factors other than 1, we have: \[ \text{GCD}(4, 3) = 1 \] 4. **Substitute the values into the LCM formula:** \[ \text{LCM}(4, 3) = \frac{4 \times 3}{1} = 12 \] Thus, the first day when Tia's and Jay's visits will coincide is in \( 12 \) days.