Find the Product of Two Numbers Using Given HCF and LCM Conditions

Video Explanation

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Solution

Question: If the sum of the LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, find the product of the two numbers.

(a) 203400    (b) 194400    (c) 198400    (d) 205400

Step 1: Assume HCF and LCM

Let the HCF of the two numbers = x

Then, LCM = x + 900

Step 2: Use the Given Sum

HCF + LCM = 1260

x + (x + 900) = 1260

2x + 900 = 1260

2x = 360

x = 180

∴ HCF = 180 and LCM = 1080

Step 3: Use the HCF–LCM Property

Product of two numbers = HCF × LCM

= 180 × 1080

= 194400

Final Answer

✔ The product of the two numbers is 194400.

✔ Correct option: (b) 194400

Conclusion

Thus, using the relationship between HCF and LCM, the product of the given two numbers is 194400.