The number nearest to 43528 divisible by each of 25, 50 and 75 is

Options

A. 43500
B. 43650
C. 43600
D. 43550

Answer

To find the number nearest to 43,528 that is divisible by 25, 50, and 75, we can follow these steps:

### Step 1: Find the LCM of 25, 50, and 75
To find the least common multiple (LCM) of these numbers, we can use their prime factorization:
- 25 = 5²
- 50 = 2 × 5²
- 75 = 3 × 5²

The LCM is found by taking the highest power of each prime factor:
- For 2: highest power is 2¹ from 50
- For 3: highest power is 3¹ from 75
- For 5: highest power is 5² from all three numbers

Thus, the LCM is:
\[ LCM = 2^1 × 3^1 × 5^2 = 2 × 3 × 25 = 150 \]

### Step 2: Divide 43,528 by the LCM (150)
Now we divide 43,528 by 150 to find how many times it fits:
\[ 43,528 ÷ 150 = 290.1867 \]
This means 150 fits into 43,528 approximately 290 times.

### Step 3: Calculate the two nearest multiples of 150
Now we calculate the two nearest multiples of 150:
- The lower multiple:
\[ 150 × 290 = 43,500 \]
- The upper multiple:
\[ 150 × 291 = 43,650 \]

### Step 4: Determine which multiple is closer to 43,528
Now we compare the differences:
- Difference from 43,500:
\[ 43,528 - 43,500 = 28 \]
- Difference from 43,650:
\[ 43,650 - 43,528 = 122 \]

Since 28 is less than 122, 43,500 is closer to 43,528.

### Final Answer
The number nearest to 43,528 that is divisible by 25, 50, and 75 is:
\[ \boxed{43,500} \]

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