Laura goes to the grocery store every 5 days and Tim goes to the same grocery store every 6 days. If Laura and Tim both went to the grocery store today, when is the next time they will both go to the grocery store on the same day?

Laura goes to the grocery store every 5 days and Tim goes to the same grocery store every 6 days. If Laura and Tim both went to the grocery store today, when is the next time they will both go to the grocery store on the same day?

Detailed Explanation

To determine when Laura and Tim will both go to the grocery store on the same day again, we need to find the least common multiple of the two intervals: 5 days and 6 days.

Calculate the least common multiple using the following steps:

- Find the prime factorization of each number: 5 = 5 and 6 = 2 × 3

- Find the highest power of each prime factor: \(5^1\) and \(2^1 × 3^1\)

- Multiply the prime factors together: \(5^1 × 2^1 × 3^1\) = 30

The least common multiple of 5 and 6 is 30.

This means that after 30 days, both Laura and Tim will go to the grocery store on the same day again.

Calculate the least common multiple using the following steps:

- Find the prime factorization of each number: 5 = 5 and 6 = 2 × 3

- Find the highest power of each prime factor: \(5^1\) and \(2^1 × 3^1\)

- Multiply the prime factors together: \(5^1 × 2^1 × 3^1\) = 30

The least common multiple of 5 and 6 is 30.

This means that after 30 days, both Laura and Tim will go to the grocery store on the same day again.