What least number must be added to 2535 so that the sum is completely divisible by 27?

Options

A. a)3
B. b)26
C. c)10
D. d)12

Answer

To find the least number that must be added to 2535 so that the sum is completely divisible by 27, we can follow these steps:

### Step 1: Divide 2535 by 27
First, we need to determine how many times 27 fits into 2535. We perform the division:

\[ 2535 \div 27 \approx 93.0 \]

### Step 2: Calculate the product of the quotient and 27
Next, we multiply the integer part of the quotient (93) by 27 to find the largest multiple of 27 that is less than or equal to 2535:

\[ 93 \times 27 = 2511 \]

### Step 3: Find the remainder
Now, we find the remainder when we subtract this product from 2535:

\[ 2535 - 2511 = 24 \]

### Step 4: Determine how much to add to reach the next multiple of 27
To make 2535 divisible by 27, we need to reach the next multiple of 27. The next multiple can be calculated by adding \(27 - 24\):

\[ 27 - 24 = 3 \]

### Conclusion
Thus, the least number that must be added to 2535 to make it divisible by 27 is:

\[ \text{Least number to add} = 3 \]