Question

The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of two numbers is 1:4, then the larger among two numbers is:

• A. 88
• B. 28
• C. 48
• D. 84

Answer 1

The Correct Option is D

To find the larger of the two numbers given their LCM, HCF, and ratio, you can use the relationship between LCM, HCF, and the product of the numbers. Here's the step-by-step solution: 

1. The product of two numbers is given by the formula: \(a \times b = \text{LCM}(a, b) \times \text{HCF}(a, b)\).
2. Here, the LCM is 84 and the HCF is 21. Therefore: \(a \times b = 84 \times 21\).
3. Calculating the product: \(a \times b = 1764\).
4. Given the ratio of the two numbers is 1:4, let the numbers be \(x\) and \(4x\) respectively.
5. Using the product relation: \(x \times 4x = 1764\).
6. This simplifies to: \(4x^2 = 1764\).
7. Solving for \(x\): \(x^2 = 441\).
8. Taking the square root of both sides: \(x = 21\).
9. The two numbers are \(21\) and \(4 \times 21 = 84\).
10. Therefore, the larger number is 84.
11. The correct answer is \(84\).