The LCM of 0.04, 0.16 and 2.4 is

Options

A. A)4.8
B. B)2.4
C. C)0.24
D. D)3.6

Answer

To find the LCM of the numbers 0.04, 0.16, and 2.4, we will follow these steps:

### Step 1: Convert decimal numbers to fractions
- Convert 0.04 to a fraction:
\[ 0.04 = \frac{4}{100} = \frac{1}{25} \]
- Convert 0.16 to a fraction:
\[ 0.16 = \frac{16}{100} = \frac{4}{25} \]
- Convert 2.4 to a fraction:
\[ 2.4 = \frac{24}{10} = \frac{12}{5} \]

### Step 2: Identify the numerators and denominators
- The numerators are: 1, 4, and 12
- The denominators are: 25, 25, and 5

### Step 3: Calculate the LCM of the numerators
- Find the LCM of 1, 4, and 12:
- The prime factors are:
- 1: (no prime factors)
- 4: \(2^2\)
- 12: \(2^2 \times 3\)
- The LCM is determined by taking the highest power of each prime:
- \(2^2\) from 4 and \(3^1\) from 12
- Thus,
\[ \text{LCM}(1, 4, 12) = 2^2 \times 3^1 = 4 \times 3 = 12 \]

### Step 4: Calculate the LCM of the denominators
- Find the LCM of 25, 25, and 5:
- The prime factors are:
- 25: \(5^2\)
- 5: \(5^1\)
- The LCM is determined by taking the highest power of each prime:
- \(5^2\) from 25
- Thus,
\[ \text{LCM}(25, 25, 5) = 25 \]

### Step 5: Combine the results to find the LCM of the fractions
- The LCM of the fractions is given by:
\[ \text{LCM} = \frac{\text{LCM of numerators}}{\text{LCM of denominators}} = \frac{12}{25} \]

### Step 6: Convert the LCM back to decimal form
- To convert \(\frac{12}{25}\) to decimal:
\[ \frac{12}{25} = 0.48 \]

### Final Answer
The LCM of 0.04, 0.16, and 2.4 is 0.48.

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