Answer please give me the answers in 4 steps only: The times on two clocks are checked regularly. One clock is checked every 6 days. The other clock is checked every 8 days. Both clocks are checked on 1st January 2021. Find the number of days during 2021 when both clocks will be checked on the same day. There are 365 days in 2021

To find the number of days in 2021 when both clocks will be checked on the same day, we can follow these steps:

1. **Determine the Checking Frequency**:
   - Clock A is checked every 6 days.
   - Clock B is checked every 8 days.

2. **Find the Least Common Multiple (LCM)**:
   - Calculate the LCM of 6 and 8.
   - The prime factorization gives:
     - \(6 = 2 \times 3\)
     - \(8 = 2^3\)
   - LCM = \(2^3 \times 3 = 24\).

3. **Calculate the Days in 2021**:
   - The clocks will be checked together every 24 days.
   - Starting from January 1, 2021, calculate the days: \(1, 25, 49, 73, \ldots\) up to 365.

4. **Count the Instances**:
   - The sequence of days can be represented as \(1 + 24n\), where \(n\) is a non-negative integer.
   - Set up the equation \(1 + 24n \leq 365\).
   - This gives \(24n \leq 364 \rightarrow n \leq 15.166\). Thus, \(n\) can take values from 0 to 15, giving us 16 instances.

**Final Answer**: The clocks will be checked on the same day **16 times** in 2021.

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How do you calculate the LCM of two numbers?
2. What are the implications of checking clocks at different intervals?
3. Can this method be applied to more than two clocks?
4. How would the answer change if there were 366 days in the year?
5. What are real-life applications of finding the LCM? 

**Tip**: When calculating LCM, always consider the highest power of each prime factor involved.

The times on two clocks are checked regularly. One clock is checked every 6 days. The other clock is checked every 8 days. Both clocks are checked on 1st January 2021. Find the number of days during 2021 when both clocks will be checked on the same day. There are 365 days in 2021.

Discover how to find the number of days in 2021 when two clocks, checked every 6 and 8 days respectively, are checked on the same day. This problem involves calculating the least common multiple and provides a detailed step-by-step solution. Perfect for Grades 7-9 math students.

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