What is the product of Least Common Multiple and Highest Common Factor of 3200…

Property: For any two positive integers A and B, the product of their HCF and LCM is equal to the product of the numbers: HCF × LCM = A × B.

Given Numbers: A = 3200, B = 1250.

Prime Factorization:

3200 = 32 × 100 = 2^5 × (2^2 × 5^2) = 2^7 × 5^2.

1250 = 125 × 10 = 5^3 × (2 × 5) = 2^1 × 5^4.

Product Calculation:

A × B = (2^7 × 5^2) × (2^1 × 5^4).

Combine exponents: 2^(7+1) × 5^(2+4) = 2^8 × 5^6.

Final Answer: Option 4 (2^8 × 5^6)