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

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

UpStudy AI · Accepted Answer

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.
The first day when Tia and Jay will visit their grandmother together is on the 12th day.

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?

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