Question

gretta eats oatmeal for breakfast every 4 days, chicken strips for lunch every 3 days, and chicken alfredo for dinner every 7 days. if today is april 1 and she had all 3 things today, how many days will pass before she will have all 3 items in the same day again?

Explanation:

Step1: Identify the problem type

We need to find the least common multiple (LCM) of 4, 3, and 7 since we want to know when Gretta will have all three meals on the same day again, which is the smallest number that is a multiple of all three intervals.

Step2: Check if the numbers are prime or can be factored

• 3 is a prime number: \(3 = 3\)
• 4 can be factored into \(2\times2\)
• 7 is a prime number: \(7 = 7\)

Step3: Calculate the LCM

To find the LCM, we take the highest power of each prime number that appears in the factorizations.

• For prime 2: the highest power is \(2^2\) (from 4)
• For prime 3: the highest power is \(3^1\) (from 3)
• For prime 7: the highest power is \(7^1\) (from 7)

Then, we multiply these together: \(LCM = 2^2\times3\times7\)

Step4: Compute the value

First, calculate \(2^2 = 4\). Then, multiply \(4\times3 = 12\), and then \(12\times7 = 84\).

Answer:

84