Question

Lily and Dustin each have a band. Lily's band plays songs in sets of 5 and Dustin's band plays songs in sets of 10. After performing together, both bands realize that they have played the same number of songs. What is the smallest number of songs each band could have performed?

Answer 1

10 songs

Step-by-step explanation:

Based on the scenario being described we seem to need to find the greatest common multiple of these two bands. This is done simply by multiplying the songs in each set of each band by every factor (1 2 3 4 5 ...) until you find a common product between each band. Like so...

5*1 = 5 10*1 = 10

5*2 = 10

We can see that the first and smallest number of songs that each band could have performed would be 10 songs. Meaning that Lily's Band played two (2) sets and Dustin's Band played one (1) set.