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The LCM of the smallest multiple of 4 an...

The LCM of the smallest multiple of 4 and smallest multiple of 6 is:

A

6

B

12

C

24

D

48

Text Solution

AI Generated Solution

The correct Answer is:
To find the LCM (Least Common Multiple) of the smallest multiple of 4 and the smallest multiple of 6, we can follow these steps: ### Step 1: Identify the smallest multiples - The smallest multiple of 4 is **4** itself. - The smallest multiple of 6 is **6** itself. ### Step 2: Find the prime factorization of each number - The prime factorization of **4** is: \[ 4 = 2^2 \] - The prime factorization of **6** is: \[ 6 = 2^1 \times 3^1 \] ### Step 3: Determine the maximum power of each prime factor - For the prime number **2**: - The maximum power from 4 is \(2^2\). - The maximum power from 6 is \(2^1\). - Therefore, we take \(2^2\). - For the prime number **3**: - The maximum power from 4 is \(3^0\) (since 4 does not have 3 as a factor). - The maximum power from 6 is \(3^1\). - Therefore, we take \(3^1\). ### Step 4: Calculate the LCM - Now, we multiply the highest powers of all prime factors: \[ \text{LCM} = 2^2 \times 3^1 = 4 \times 3 = 12 \] ### Final Answer Thus, the LCM of the smallest multiple of 4 and the smallest multiple of 6 is **12**. ---
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