The LCM of `(5)/(12),(6)/(5),(3)/(2)and (4)/(17)` is

Options

A. 60
B. `(1)/(60)`
C. 180
D. None of these

Explanation

To find the LCM of the fractions \(\frac{5}{12}, \frac{6}{5}, \frac{3}{2}, \frac{4}{17}\), we can use the formula for the LCM of fractions:

\[ \text{LCM}\left(\frac{a}{b}, \frac{c}{d}, \frac{e}{f}, \frac{g}{h}\right) = \frac{\text{LCM}(a, c, e, g)}{\text{HCF}(b, d, f, h)} \]

### Step 1: Identify the numerators and denominators
The numerators are: \(5, 6, 3, 4\)
The denominators are: \(12, 5, 2, 17\)

### Step 2: Find the LCM of the numerators
To find the LCM of \(5, 6, 3, 4\):

- Prime factorization:
- \(5 = 5^1\)
- \(6 = 2^1 \times 3^1\)
- \(3 = 3^1\)
- \(4 = 2^2\)

- Take the highest power of each prime:
- \(2^2\) (from 4)
- \(3^1\) (from 6 or 3)
- \(5^1\) (from 5)

Now, calculate the LCM:
\[ \text{LCM} = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \]

### Step 3: Find the HCF of the denominators
To find the HCF of \(12, 5, 2, 17\):

- Prime factorization:
- \(12 = 2^2 \times 3^1\)
- \(5 = 5^1\)
- \(2 = 2^1\)
- \(17 = 17^1\)

- The only common factor is \(1\) since there are no common prime factors.

So, \(\text{HCF} = 1\).

### Step 4: Apply the LCM formula for fractions
Now, substitute the values into the formula:
\[ \text{LCM}\left(\frac{5}{12}, \frac{6}{5}, \frac{3}{2}, \frac{4}{17}\right) = \frac{\text{LCM}(5, 6, 3, 4)}{\text{HCF}(12, 5, 2, 17)} = \frac{60}{1} = 60 \]

### Final Answer
The LCM of the fractions \(\frac{5}{12}, \frac{6}{5}, \frac{3}{2}, \frac{4}{17}\) is \(60\).

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