Frank has baseball practice every 4th day and choir practice every 6th day. When will he have baseball and choir practice on the same day?
This is just a Lowest Common Multiple (LCM) question.
So the first time would be 12 days, then 24, 36, etc days from your day of reference.
look at it this way:
days for baseball: 4, 8, 12, 16, 20, 24, 28, 32, 36, ..
days for choir: 6,12, 18, 24, 30, 36, ...
Which days are common?
To find the day when Frank will have baseball and choir practice on the same day, we need to find the least common multiple (LCM) of the two practice intervals, which are 4 days and 6 days.
The prime factorization of 4 is 2^2, and the prime factorization of 6 is 2 * 3.
To find the LCM, we take the highest powers of each prime factor that appear in either factorization:
- 2^2 * 3 = 12.
Therefore, the LCM of 4 and 6 is 12.
Thus, Frank will have baseball and choir practice on the same day every 12th day.
To find out when Frank will have baseball and choir practice on the same day, we need to find the common multiples of 4 and 6, as these represent the number of days between each practice.
One way to find the common multiples is by listing the multiples of each number and looking for a common value:
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, ...
- The multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
By looking at the list, we can see that the first common multiple of 4 and 6 is 12. This means that Frank will have baseball and choir practice on the 12th day.
Therefore, Frank will have baseball and choir practice on the same day after 12 days.