Question

Mai must choose a number between 49 and 95 that is a multiple of 3, 8, and 12. Write all the numbers that she could choose. If there is more than one number, seperate them with commas.

Answer 1

72

Step-by-step explanation:

To choose a number between 49 and 95 that is a multiple of 3, 8, and 12, the first step is to find the lowest common multiple of the three numbers.

Begin by expressing them as a product of their prime factors:

`\begin{gathered} 3=3 \\ 8=2^3 \\ 12=2^2*3 \\ \text{LCM}=2^3*3=24 \end{gathered}`

Next, we find multiples of the L.C.M in between 49 and 95.

`\begin{gathered} 24*2=48 \\ 24*3=72 \\ 24*4=96 \end{gathered}`

The only number that she could choose is 72.