Question

cher eats eggs for breakfast every 5 days, a ham sandwich for lunch every 3 days, and spaghetti for dinner every 7 days. if today is december 10 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

This is a problem about finding the least common multiple (LCM) of three numbers: 5, 3, and 7.

Step2: Recall the LCM formula for coprime numbers

Since 3, 5, and 7 are all prime numbers (and thus coprime to each other), the LCM of coprime numbers is the product of the numbers. So we calculate \( LCM(3, 5, 7) = 3\times5\times7 \).

Step3: Calculate the product

\( 3\times5 = 15 \), then \( 15\times7 = 105 \).

Answer:

105