You have violin lessons every 6 days and singing lessons every 20 days. Today you have both lessons. In how many days will you have both lessons on the same day again
LCM(6,20) = 60
To determine when you will have both violin and singing lessons on the same day again, you need to find the least common multiple (LCM) of 6 and 20. The LCM is the smallest value that is divisible by both numbers.
First, list out the multiples of each number until you find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 20: 20, 40, 60, ...
From the lists above, you can see that 24 is the smallest number that is a multiple of both 6 and 20. Therefore, you will have both lessons on the same day again in 24 days.
So, in 24 days, you will have both violin and singing lessons on the same day.