What is the product of Least Common Multiple and Highest Common Factor of 3200…
2021
What is the product of Least Common Multiple and Highest Common Factor of 3200 and 1250?
Answer: D. 28 × 56 — 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…
- A.
21 × 52
- B.
25 × 53
- C.
28 × 54
- D.
28 × 56
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Correct answer: D
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)