To find the least number that must be added to 893304 to obtain a perfect square, we can use a systematic approach to find the square root of the given number.

1. Prime Factorization of 893304:
To find the square root of 893304, we need to break it down into its prime factors. The prime factorization of 893304 is:

893304 = 2^3 × 3^2 × 7 × 11 × 13

2. Grouping the Factors:
Next, we group the prime factors in pairs of the same factor:

893304 = (2^2 × 3 × 7 × 11 × 13) × (2 × 3 × 7)

3. Taking out the Perfect Squares:
We take out perfect squares from each group of factors:

893304 = (2^2 × 3^2 × 7^2) × (2 × 3 × 7) = (2^2 × 3^2 × 7^2) × (2 × 3 × 7)

4. Simplifying the Expression:
Now, we simplify the expression by multiplying the square roots of the perfect squares:

√893304 = √(2^2 × 3^2 × 7^2) × √(2 × 3 × 7)

= (2 × 3 × 7) × √(2 × 3 × 7)

= 42 × √(2 × 3 × 7)

= 42 × √(42)

= 42 × √(2^1 × 3^1 × 7^1)

= 42 × (2^1/2 × 3^1/2 × 7^1/2)

5. Finding the Perfect Square:
We see that the expression contains the square root of 42. We need to find the least number that, when added to 893304, will make it a perfect square. To do this, we need to find the next perfect square greater than 893304.

The next perfect square greater than 893304 is 893521, which is equal to (299^2). Therefore, the least number that must be added to 893304 to obtain a perfect square is:

893521 - 893304 = 217

So, the correct answer is option 'A' - 1612.