Questions: Debra must choose a number between 49 and 95 that is a multiple of 2,3 , and 9 . Write all the numbers that she could choose. If there is more than one number, separate them with commas.

Debra must choose a number between 49 and 95 that is a multiple of 2,3 , and 9 . Write all the numbers that she could choose. If there is more than one number, separate them with commas.

Transcript text: Debra must choose a number between 49 and 95 that is a multiple of 2,3 , and 9 . Write all the numbers that she could choose. If there is more than one number, separate them with commas.

Solution

Solution Steps

To find a number between 49 and 95 that is a multiple of 2, 3, and 9, we need to find the least common multiple (LCM) of these numbers. Since 9 is already a multiple of 3, we only need to consider the LCM of 2 and 9, which is 18. We then list all multiples of 18 within the given range.

Step 1: Determine the Range and LCM

We need to find numbers between \(49\) and \(95\) that are multiples of \(2\), \(3\), and \(9\). The least common multiple (LCM) of \(2\) and \(9\) is calculated as follows: \[ \text{lcm}(2, 9) = 18 \]

Step 2: Identify Multiples of the LCM

Next, we identify the multiples of \(18\) that fall within the range \(49\) to \(95\). The multiples of \(18\) in this range are: \[ 54, 72, 90 \]