A number, when divided by 8, 12 and 15, gives always remainder 5. Then number is:

Options

A. 150
B. 125
C. 120
D. 130

Answer

To find a number that, when divided by 8, 12, and 15, always gives a remainder of 5, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Divisors**: The numbers we are dividing by are 8, 12, and 15.

2. **Calculate the Least Common Multiple (LCM)**:
- To find the LCM of 8, 12, and 15, we first find the prime factorization of each number:
- 8 = \(2^3\)
- 12 = \(2^2 \times 3\)
- 15 = \(3 \times 5\)
- Now, take the highest power of each prime factor:
- For 2: the highest power is \(2^3\) (from 8)
- For 3: the highest power is \(3^1\) (from both 12 and 15)
- For 5: the highest power is \(5^1\) (from 15)
- Therefore, the LCM is:
\[ LCM = 2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 \]
- Calculate this step by step:
- \(8 \times 3 = 24\)
- \(24 \times 5 = 120\)
- Thus, \(LCM(8, 12, 15) = 120\).

3. **Adjust for the Remainder**:
- Since we want the number to give a remainder of 5 when divided by 8, 12, and 15, we add 5 to the LCM:
\[ \text{Number} = LCM + 5 = 120 + 5 = 125 \]

4. **Conclusion**:
- The number we are looking for is **125**.