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If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers?
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If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 ...
Given Conditions
The problem states two conditions involving two numbers, let's denote their HCF as 'h' and LCM as 'l':
- The sum of HCF and LCM is 1260:
h + l = 1260
- The LCM is 900 more than the HCF:
l = h + 900
Setting Up the Equations
We can substitute the second condition into the first:
- h + (h + 900) = 1260
This simplifies to:
- 2h + 900 = 1260
Solving for HCF
Now, we can solve for 'h':
- 2h = 1260 - 900
- 2h = 360
- h = 180
Finding the LCM
Now that we have the HCF, we can find the LCM:
- l = h + 900
- l = 180 + 900
- l = 1080
Finding the Product of the Two Numbers
The relationship between the product of two numbers (a and b), their HCF (h), and their LCM (l) is given by:
- Product = HCF * LCM
Substituting the values we found:
- Product = 180 * 1080
Calculating the Product
To find the product:
- Product = 194400
Final Answer
Thus, the product of the two numbers is 194400.
The problem states two conditions involving two numbers, let's denote their HCF as 'h' and LCM as 'l':
- The sum of HCF and LCM is 1260:
h + l = 1260
- The LCM is 900 more than the HCF:
l = h + 900
Setting Up the Equations
We can substitute the second condition into the first:
- h + (h + 900) = 1260
This simplifies to:
- 2h + 900 = 1260
Solving for HCF
Now, we can solve for 'h':
- 2h = 1260 - 900
- 2h = 360
- h = 180
Finding the LCM
Now that we have the HCF, we can find the LCM:
- l = h + 900
- l = 180 + 900
- l = 1080
Finding the Product of the Two Numbers
The relationship between the product of two numbers (a and b), their HCF (h), and their LCM (l) is given by:
- Product = HCF * LCM
Substituting the values we found:
- Product = 180 * 1080
Calculating the Product
To find the product:
- Product = 194400
Final Answer
Thus, the product of the two numbers is 194400.
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If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers?
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If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers?.
If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of lcm and hcf of two numbers is 1260 and their lcm is 900 more than their hcf, then find the product of two numbers?.
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