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The HCF and LCM of the two numbers are 45 and 270, respectively. If the ratio of the two numbers is 2:3 and the smaller of the two numbers is X, then find X2.
- a)2025
- b)4225
- c)8100
- d)18225
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The HCF and LCM of the two numbers are 45 and 270, respectively. If t...
We know that
Product of numbers = product of lcm and hcf
2y × 3y = 45 × 270
y2 = 45 × 45
y = 45
then smaller no.
X = 2 × 45 = 90
X2 = (90)2 = 8100
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The HCF and LCM of the two numbers are 45 and 270, respectively. If t...
Understanding HCF and LCM
HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of two numbers can be calculated using the formula:
HCF × LCM = Product of the two numbers.
Given:
- HCF = 45
- LCM = 270
Calculating the Product of the Two Numbers
Using the formula:
- Product = HCF × LCM
- Product = 45 × 270
- Product = 12150
Using the Ratio of the Two Numbers
The ratio of the two numbers is given as 2:3. Let's denote the two numbers as:
- Smaller number (X) = 2k
- Larger number = 3k
Setting Up the Equation
From the product we calculated:
- (2k) × (3k) = 12150
- 6k² = 12150
Finding k
To find k:
- k² = 12150 / 6
- k² = 2025
- k = √2025 = 45
Finding the Smaller Number (X)
Now, substituting k back to find X:
- X = 2k = 2 × 45 = 90
Calculating X²
Now, we find X²:
- X² = 90² = 8100
Conclusion
The value of X² is 8100, which confirms that the correct answer is option 'C'.
HCF (Highest Common Factor) and LCM (Lowest Common Multiple) of two numbers can be calculated using the formula:
HCF × LCM = Product of the two numbers.
Given:
- HCF = 45
- LCM = 270
Calculating the Product of the Two Numbers
Using the formula:
- Product = HCF × LCM
- Product = 45 × 270
- Product = 12150
Using the Ratio of the Two Numbers
The ratio of the two numbers is given as 2:3. Let's denote the two numbers as:
- Smaller number (X) = 2k
- Larger number = 3k
Setting Up the Equation
From the product we calculated:
- (2k) × (3k) = 12150
- 6k² = 12150
Finding k
To find k:
- k² = 12150 / 6
- k² = 2025
- k = √2025 = 45
Finding the Smaller Number (X)
Now, substituting k back to find X:
- X = 2k = 2 × 45 = 90
Calculating X²
Now, we find X²:
- X² = 90² = 8100
Conclusion
The value of X² is 8100, which confirms that the correct answer is option 'C'.
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The HCF and LCM of the two numbers are 45 and 270, respectively. If the ratio of the two numbers is 2:3 and the smaller of the two numbers is X, then find X2.a)2025b)4225c)8100d)18225Correct answer is option 'C'. Can you explain this answer?
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Solutions for The HCF and LCM of the two numbers are 45 and 270, respectively. If the ratio of the two numbers is 2:3 and the smaller of the two numbers is X, then find X2.a)2025b)4225c)8100d)18225Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
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