Question

You have violin lessons every 4th day and singing lessons every 5th day. Today you have both lessons after school. In how many days will you have both lessons on the same day again? (LCM)

A) 9
B) 10
C) 15
D) 20

Answer 1

The LCM of 4 and 5 is found by listing the multiples of both numbers and identifying the smallest common multiple, which is 20 days. So, the student will have both lessons on the same day again in 20 days.

Step-by-step explanation:

To determine when the student will have both violin and singing lessons on the same day again, we need to find the Least Common Multiple (LCM) of the numbers 4 and 5. The LCM of two numbers is the smallest number that is a multiple of both numbers. Since the student has violin lessons every 4th day and singing lessons every 5th day, we are looking for the smallest number that both 4 and 5 will divide into evenly.

Listing the multiples of 4: 4, 8, 12, 16, 20, ...

Listing the multiples of 5: 5, 10, 15, 20, ...

The smallest common multiple of both 4 and 5 is 20. This means that the student will have both violin and singing lessons on the same day again in 20 days.

Therefore, the correct answer is D) 20.