Rosita earns money by walking dogs after school and on the weekends. She walks Madeline every other day, Buddy every forth day, and Ernie every third day. Today she walked all thee dogs. What day did Rosita walk all three dogs?

Rosita will walk all three dogs in 12 days.

Explanation:

Madeline is walked every other day means every two days: 2.

Buddy is walked every fourth day: 4.

Ernie is walked every third day: 3.

You need to find the least common multiple (LCM) of 2, 4, 3.

Decompose each number into its prime factors:

2 = 2 4 = 2² 3 = 3

The LCM is the product of the common factors and non common factors each raised to its the greatest power:

LCM = 2² * 3 = 12

Then, Rosita will walk all three dogs in 12 days.