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 will follow these steps:

### Step 1: Remove the Decimals
First, we need to convert the decimal numbers into fractions to make calculations easier. We can do this by multiplying each number by 10 to eliminate the decimal point.

- 3.6 = 36/10
- 1.2 = 12/10
- 4.8 = 48/10

### Step 2: Find the LCM of the Numerators
Next, we will find the LCM of the numerators (36, 12, and 48).

To find the LCM, we can use the prime factorization method:

- **36** = 2^2 × 3^2
- **12** = 2^2 × 3^1
- **48** = 2^4 × 3^1

Now, we take the highest power of each prime factor:

- For 2: The highest power is 2^4 (from 48).
- For 3: The highest power is 3^2 (from 36).

Thus, the LCM of 36, 12, and 48 is:
\[ LCM = 2^4 × 3^2 = 16 × 9 = 144 \]

### Step 3: Find the HCF of the Denominators
Now, we need to find the HCF (Highest Common Factor) of the denominators. Since all denominators are 10, the HCF is:
\[ HCF = 10 \]

### Step 4: Calculate the LCM of the Fractions
The LCM of the fractions is given by the formula:
\[ LCM = \frac{LCM \text{ of numerators}}{HCF \text{ of denominators}} \]
Substituting the values we have:
\[ LCM = \frac{144}{10} = 14.4 \]

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

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