Question

Frida, Matt, and Sharice attend a baking class at different times. Frida attends class every sixth day, Matt attends every seventh day, and Sharice attends every ninth day. On what day will they all be at the baking class together?

The 168th day.

The 42nd day.

The 84th day.

The 126th day.

Answer 1

To determine when Frida, Matt, and Sharice will all be at the baking class together, we need to find the least common multiple (LCM) of their attendance schedules: Frida attends every 6 days, Matt every 7 days, and Sharice every 9 days.

First, we can calculate the prime factorization of each number:

- 6 = 2 × 3
- 7 = 7 (7 is already prime)
- 9 = 3²

Next, the LCM is found by taking the highest power of each prime number from the factorization:

- The highest power of 2 is \( 2^1 \) from the number 6.
- The highest power of 3 is \( 3^2 \) from the number 9.
- The highest power of 7 is \( 7^1 \) from the number 7.

Now, we calculate the LCM:

\[
\text{LCM} = 2^1 \times 3^2 \times 7^1
\]

Calculating this step by step:

1. \( 3^2 = 9 \)
2. \( 2^1 = 2 \)
3. So, \( 2 \times 9 = 18 \)
4. Finally, \( 18 \times 7 = 126 \)

Thus, the least common multiple of 6, 7, and 9 is **126**.

Therefore, Frida, Matt, and Sharice will all be at the baking class together on the **126th day**.