Tanya gives away to each of four girls `1/12, 5/18, 7/30, 7/48` of apples in a basket and has only just enough apples to be able to do so without dividing an apple. The minimum number of apples she has in her basket:

Options

A. 250
B. 720
C. 750
D. none

Answer

To find the minimum number of apples Tanya has in her basket, we need to determine the least common multiple (LCM) of the denominators of the fractions given. The fractions are:

1. \( \frac{1}{12} \)
2. \( \frac{5}{18} \)
3. \( \frac{7}{30} \)
4. \( \frac{7}{48} \)

### Step 1: Identify the denominators
The denominators are: 12, 18, 30, and 48.

### Step 2: Prime factorization of each denominator
- **12**: \( 12 = 2^2 \times 3^1 \)
- **18**: \( 18 = 2^1 \times 3^2 \)
- **30**: \( 30 = 2^1 \times 3^1 \times 5^1 \)
- **48**: \( 48 = 2^4 \times 3^1 \)

### Step 3: Determine 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 18).
- For \( 5 \): The highest power is \( 5^1 \) (from 30).

### Step 4: Calculate the LCM
The LCM is found by multiplying the highest powers of all prime factors:

\[ \text{LCM} = 2^4 \times 3^2 \times 5^1 \]

Calculating this step-by-step:
1. \( 2^4 = 16 \)
2. \( 3^2 = 9 \)
3. \( 5^1 = 5 \)

Now multiply these together:

\[ 16 \times 9 = 144 \]
\[ 144 \times 5 = 720 \]

### Conclusion
The minimum number of apples Tanya has in her basket is **720**.