Question

Meagan is taking piano and gymnastics lessons. She has a piano lesson every 13 days and a gymnastics lesson every 6 days. When will she have both on the same day?

a) Every 39 days
b) Every 26 days
c) Every 78 days
d) Every 156 days.

Answer 1

The least common multiple (LCM) of Meagan's lesson intervals, 13 days and 6 days, is 78. Meagan will have both piano and gymnastics lessons on the same day every 78 days.

Step-by-step explanation:

The question is asking to find the common multiple of the two lesson intervals: piano lessons every 13 days and gymnastics lessons every 6 days. To find when Meagan will have both lessons on the same day, we need to calculate the least common multiple (LCM) of 13 and 6.

• The multiples of 13 are 13, 26, 39, 52, 65, 78, and so on.
• The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, and so on.

By examining the lists, we can see that the LCM of 13 and 6 is 78. Therefore, Meagan will have both piano and gymnastics lessons on the same day every 78 days.

The correct answer is c) Every 78 days.