What is the least perfect square divisible by 8, 9 and 10?Options :A] 4000B] 6400C] 3600D] 14641

The least perfect square divisible by 8, 9 and 10 is found by:

1. Prime factorizing the numbers:

   • 8 = 2^3
   • 9 = 3^2
   • 10 = 2*5

2. Taking the highest power of each prime from the factorizations:

   • For 2, the highest power is 3 (from 8)
   • For 3, the highest power is 2 (from 9)
   • For 5, the highest power is 1 (from 10)

3. Multiplying these together gives the least common multiple (LCM):

   • LCM = 2^3 * 3^2 * 5 = 360

4. But we need the least perfect square, so each power in the prime factorization should be even. Currently, the power of 5 is odd. To make it even, we multiply by another 5, giving:

   • LCM = 2^3 * 3^2 * 5^2 = 3600

So, the least perfect square divisible by 8, 9 and 10 is 3600. Therefore, the answer is C] 3600.