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Video: Solving Word Problems by Finding the Lowest Common Multiple

Kathryn Kingham

Noah goes to the supermarket every 14 days, and Diane goes to the same supermarket every 21 days. If Noah and Diane meet at the supermarket on a particular day, how many days will pass before they meet each other again at the supermarket?

02:20

Video Transcript

Noah goes to the supermarket every 14 days, and Diane goes to the same supermarket every 21 days. If Noah and Diane meet at the supermarket on a particular day, how many days will pass before they meet each other again at the supermarket?

Let’s start by highlighting what we know. We know that Noah is at the supermarket every 14 days and that Diane is at the same supermarket every 21 days. We also know that on a particular day they both were at the supermarket on the same day.

This is a question of least common multiple. Noah goes to the supermarket first on day 14, and after that day 28, and then on day 42, and then 56. These are the first four multiples of 14.

The first time Diane is going to the supermarket is day 21, and after that day 42, and then day 63. The fourth multiple of 21 is 84.

Now we’re looking for a multiple that is common among the days that Noah goes and the days that Diane goes to the grocery store. We notice that 42 is a multiple of 14 and 21. What this tells us is that every 42 days they’re both at the grocery store on the same day.

If Noah and Diane saw each other at the grocery store today, they would see each other again in 42 days. We know this is true because 42 is the least common multiple among 14 and 21. Our final answer is 42 days.