Which among the following numbers is exactly divisible by 7,11 and 13 ?

Options

A. 14993
B. 15004
C. 15015
D. 14982

Answer

To determine which number is exactly divisible by 7, 11, and 13, we can follow these steps:

### Step-by-Step Solution:

1. **Find the LCM of 7, 11, and 13**:
- Since all three numbers are prime, the least common multiple (LCM) can be found by multiplying them together.
- LCM = 7 × 11 × 13

2. **Calculate the LCM**:
- First, multiply 7 and 11:
\[ 7 \times 11 = 77 \]
- Next, multiply the result by 13:
\[ 77 \times 13 = 1001 \]
- Therefore, the LCM of 7, 11, and 13 is 1001.

3. **Check divisibility of the given numbers by 1001**:
- We need to check which of the provided numbers is divisible by 1001.
- If the numbers are not provided, we can assume a few examples or you can check the numbers given in your question.

4. **Perform the divisibility test**:
- For each number, divide it by 1001 and check if the remainder is zero.
- If the remainder is zero, that number is divisible by 7, 11, and 13.

5. **Example Check**:
- Let's say we have a number, for example, 15000.
- Divide 15000 by 1001:
\[ 15000 \div 1001 \approx 14.985 \]
- This means 15000 is not exactly divisible by 1001 since it does not yield a whole number.

6. **Subtract the remainder**:
- If a number is not divisible, you can find the remainder and subtract it from the number to find the nearest lower number that is divisible by 1001.
- For example, if 15000 gives a remainder of 5 when divided by 1001, then:
\[ 15000 - 5 = 14995 \]
- Check if 14995 is divisible by 1001:
\[ 14995 \div 1001 \approx 14.96 \]
- Continue this process until you find a number that is divisible.