Question

Rosita earns money by walking dogs after school and on weekends.She walks Madeline every other day,buddy every fourth day,and ernie every third day.Today she walked all three dogs. What day did she walk all three dogs?

Answer 1

On 12th day Rosita will walk all three dogs

Solution:

Given that Rosita earns money by walking dogs after school and on weekends

She walks Madeline every other day,buddy every fourth day,and ernie every third day

Today she walked all three dogs

To find: the day when she walked all three dogs

From given question,

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

To find the day when she walked all three dogs, we have to find the least common multiple (LCM) of 2, 4, 3

L.C.M of 2, 4, 3:

List all prime factors for each number

Prime Factorization of 2 shows:

2 is prime  => $2^1$

Prime Factorization of 3 shows:

3 is prime  => $3^1$

Prime Factorization of 4 is:

$2 \times 2 = 2^2$

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 = 12

Thus on 12th day Rosita will walk all three dogs