What least value which should be added to 1812 to make it divisible by 7, 11 and 14?

Options

A. 12
B. 36
C. 72
D. 154

Answer

To find the least value that should be added to 1812 to make it divisible by 7, 11, and 14, we can follow these steps:

### Step 1: Find the LCM of 7, 11, and 14
- Since 7, 11, and 14 have no common factors, we can find the LCM by multiplying them together.
- LCM(7, 11, 14) = 7 × 11 × 14 = 154

### Step 2: Divide 1812 by the LCM
- Now, we need to divide 1812 by 154 to find the remainder.
- Performing the division:
- 1812 ÷ 154 = 11 remainder 80
- This means 154 fits into 1812 a total of 11 times, and the remainder is 80.

### Step 3: Calculate the amount to add
- To make 1812 divisible by 154, we need to subtract the remainder from the LCM:
- Amount to add = LCM - Remainder = 154 - 80 = 74

### Step 4: Final Calculation
- Therefore, we need to add 74 to 1812:
- 1812 + 74 = 1886, which is divisible by 7, 11, and 14.

### Final Answer
The least value that should be added to 1812 to make it divisible by 7, 11, and 14 is **74**.

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