Find the least perfect square that is divisible by each of 21, 36, and 66.

Introduction:
The least perfect square divisible by given integers is found by taking the LCM, then adjusting prime exponents to be even (as required for a square).

Given Data / Assumptions:

• Numbers: 21, 36, 66

Concept / Approach:
LCM prime factorization method: 21 = 3 * 7, 36 = 2^2 * 3^2, 66 = 2 * 3 * 11. LCM collects the highest exponents across the set.

Step-by-Step Solution:
LCM = 2^2 * 3^2 * 7^1 * 11^1 = 2772To get a perfect square, make all exponents even: multiply by 7^1 * 11^1 = 77Least perfect square = 2772 * 77 = 213444

Verification / Alternative check:
Prime factors of 213444 are 2^2 * 3^2 * 7^2 * 11^2, clearly a perfect square and divisible by each original number.

Why Other Options Are Wrong:
223444, 213442, 223445: Do not correspond to the necessary exact product or square factorization.

Common Pitfalls:
Using GCD instead of LCM; forgetting to square-complete the odd exponents (7 and 11).

Final Answer:
213444