Video: Finding a Common Multiple within a Range of Two Given Numbers

The number of students in a class is between 90 and 110 and is a multiple of 2 and 5. Find the number of students.

02:21

Video Transcript

The number of students in a class is between 90 and 110 and is a multiple of two and five. Find the number of students.

In this problem, we’re given two clues about the number of students that are in a class. Our first clue is that the number of students is somewhere between 90 and 110. Our second clue is that the number is a multiple of two and five. We can use these clues to help us identify the number. We know that multiples of two always end in zero, two, four, six, or eight. They’re even numbers. Why don’t we start by listing all the even numbers between 90 and 110. 92, 94, 96, 98, 100, 102, 104, 106, and 108. There’re nine even numbers between 90 and 110. And we know the number of students in the class is one of these numbers. But which one?

As well as being a multiple of two, we know that the number is also a multiple of five. And we know that multiples of five always end in a five or a zero. All of our possible numbers are even numbers. So we’re not looking for a number that ends in a five because that would be odd. We need to look for a number between 90 and 110 that ends in a zero. There’s only one possible number 100 is between 90 and 110. 100 is an even number, so it’s a multiple of two. And 100 ends in a zero. So it must be a multiple of five. The number of students in the class, and it’s a big class, is 100.

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