Kate has a tennis lesson every 5 days. She has a basketball game every 8 days. If she has both a tennis lesson and a basketball game today, on what day will she have both again?
kate has tennis lessons on these days
now, 5, 10, 15, 20, 25 , 30, 35, 40, 45, ....
She has basketball on these days
now, 8, 16, 24, 32, 40, 48 , ...
What do you think?
thank you very much. in the 40 day.
kate has a tennis lesson every 5 days.she has a basketball game every 8 days if she has both today when will she have both of them again
Last day
To find the day when Kate will have both a tennis lesson and a basketball game again, we need to find the least common multiple (LCM) of 5 and 8. The LCM is the smallest number that is divisible by both 5 and 8.
One way to find the LCM is by listing out the multiples of both numbers:
Multiples of 5: 5, 10, 15, 20, 25, 30,...
Multiples of 8: 8, 16, 24, 32, 40,...
As we can see, the first number that appears in both lists is 40. So, Kate will have both a tennis lesson and a basketball game again in 40 days.
However, if you don't want to find the LCM manually, you can also use the formula:
LCM(a, b) = (a * b) / GCD(a, b)
where GCD(a, b) represents the greatest common divisor of a and b. In this case, the GCD of 5 and 8 is 1. Using the formula, we can calculate:
LCM(5, 8) = (5 * 8) / 1 = 40
Therefore, Kate will have both a tennis lesson and a basketball game again in 40 days.