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{:("Column A"," " ,"Column B"),("...

`{:("Column A"," " ,"Column B"),("The first number larger than 300 that is a multiple of both 6 and 8" , ,324):}`

A

If column A is larger

B

If column B is larger

C

If the columns are equal

D

If there is not enough information to decide

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of finding the first number larger than 300 that is a multiple of both 6 and 8, we can follow these steps: ### Step 1: Find the LCM of 6 and 8 To determine the first number larger than 300 that is a multiple of both 6 and 8, we first need to find the least common multiple (LCM) of these two numbers. - The prime factorization of 6 is \(2 \times 3\). - The prime factorization of 8 is \(2^3\). To find the LCM, we take the highest power of each prime factor: - For 2, the highest power is \(2^3\). - For 3, the highest power is \(3^1\). Thus, the LCM is: \[ \text{LCM}(6, 8) = 2^3 \times 3^1 = 8 \times 3 = 24 \] ### Step 2: Find the first multiple of 24 greater than 300 Next, we need to find the smallest multiple of 24 that is greater than 300. We can do this by dividing 300 by 24 and rounding up to the nearest whole number. \[ 300 \div 24 = 12.5 \] Since we need a whole number, we round up to 13. Now we multiply 24 by 13 to find the corresponding multiple: \[ 24 \times 13 = 312 \] ### Step 3: Compare with the number in Column B Now we have found that the first number larger than 300 that is a multiple of both 6 and 8 is 312. In Column B, we have the number 324. ### Step 4: Determine which column is larger Now we compare the two numbers: - Column A: 312 - Column B: 324 Since 324 is greater than 312, we conclude that Column B is larger. ### Final Answer The correct option is **B** (Column B is larger). ---
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