You have violin lessons every fourth day and singing lessons every fifth day. Today you have both lessons. In how many days will you have both lessons on the same day again?
Every 20 days. Both 4 and 5 are factors of 20 making it possible every 20 days
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To find out when you will have both lessons on the same day again, we need to find the least common multiple (LCM) of 4 and 5.
First, let's list out the multiples of 4 and 5:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
From the lists, we see that 20 is the smallest number that appears in both lists. Therefore, you will have both violin and singing lessons on the same day again in 20 days.
So the answer is 20 days.