The LCM of 3.6, 1.2 and 4.8 is

Options

A. `14.2`
B. `14.4`
C. `12.4`
D. `7.2`

Answer

To find the LCM of the numbers 3.6, 1.2, and 4.8, we can follow these steps:

### Step 1: Convert the decimal numbers to whole numbers
To make calculations easier, we can convert the decimal numbers into whole numbers by multiplying each number by 10 (since they all have one decimal place).

- \( 3.6 \times 10 = 36 \)
- \( 1.2 \times 10 = 12 \)
- \( 4.8 \times 10 = 48 \)

Now, we will find the LCM of 36, 12, and 48.

### Step 2: Find the prime factorization of each number
Next, we will find the prime factorization of each of the whole numbers:

- **36**:
- \( 36 = 2^2 \times 3^2 \)

- **12**:
- \( 12 = 2^2 \times 3^1 \)

- **48**:
- \( 48 = 2^4 \times 3^1 \)

### Step 3: Identify the highest power of each prime factor
To find the LCM, we take the highest power of each prime factor from the factorizations:

- For \( 2 \): the highest power is \( 2^4 \) (from 48)
- For \( 3 \): the highest power is \( 3^2 \) (from 36)

### Step 4: Calculate the LCM
Now, we multiply these highest powers together to find the LCM:

\[ \text{LCM} = 2^4 \times 3^2 \]

Calculating this gives:

\[ = 16 \times 9 = 144 \]

### Step 5: Adjust for the initial multiplication by 10
Since we multiplied the original numbers by 10 to convert them to whole numbers, we need to divide the LCM by 10 to adjust back:

\[ \text{Final LCM} = \frac{144}{10} = 14.4 \]

Thus, the LCM of 3.6, 1.2, and 4.8 is **14.4**.

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