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the HCF and LCM of two number s are 9 and 360 respectively. if one number is 45. writing the other number
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the HCF and LCM of two number s are 9 and 360 respectively. if one num...
Hcf* lcm = product of two numbers
Let another number be x.
9* 360 = 45 * x
X = 3240/ 45
X = 72
This question is part of UPSC exam. View all Class 10 courses
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the HCF and LCM of two number s are 9 and 360 respectively. if one num...
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the HCF and LCM of two number s are 9 and 360 respectively. if one num...
Understanding HCF and LCM
The Highest Common Factor (HCF) and the Least Common Multiple (LCM) are fundamental concepts in number theory. The relationship between two numbers can be expressed using the following formula:
Formula:
HCF × LCM = Product of the two numbers
In this case, we know:
- HCF = 9
- LCM = 360
- One number = 45
Finding the Other Number
Let's denote the unknown number as 'x'. Using the formula:
Equation:
9 × 360 = 45 × x
Now, we will calculate the left side:
Calculation:
9 × 360 = 3240
This leads us to:
Equation Rearrangement:
3240 = 45 × x
To find 'x', we will divide both sides by 45:
Calculation of x:
x = 3240 / 45
Now, perform the division:
Final Calculation:
x = 72
Conclusion
The other number is 72. Thus, the pair of numbers we are examining are 45 and 72, which have an HCF of 9 and an LCM of 360.
Verification
To verify:
- HCF of 45 and 72:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Common factors: 1, 3, 9 (HCF = 9)
- LCM of 45 and 72:
LCM = (45 × 72) / HCF = 3240 / 9 = 360
Both values confirm the calculations are correct.
The Highest Common Factor (HCF) and the Least Common Multiple (LCM) are fundamental concepts in number theory. The relationship between two numbers can be expressed using the following formula:
Formula:
HCF × LCM = Product of the two numbers
In this case, we know:
- HCF = 9
- LCM = 360
- One number = 45
Finding the Other Number
Let's denote the unknown number as 'x'. Using the formula:
Equation:
9 × 360 = 45 × x
Now, we will calculate the left side:
Calculation:
9 × 360 = 3240
This leads us to:
Equation Rearrangement:
3240 = 45 × x
To find 'x', we will divide both sides by 45:
Calculation of x:
x = 3240 / 45
Now, perform the division:
Final Calculation:
x = 72
Conclusion
The other number is 72. Thus, the pair of numbers we are examining are 45 and 72, which have an HCF of 9 and an LCM of 360.
Verification
To verify:
- HCF of 45 and 72:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Common factors: 1, 3, 9 (HCF = 9)
- LCM of 45 and 72:
LCM = (45 × 72) / HCF = 3240 / 9 = 360
Both values confirm the calculations are correct.
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the HCF and LCM of two number s are 9 and 360 respectively. if one number is 45. writing the other number Related: Facts that Matter, Real Numbers - Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about the HCF and LCM of two number s are 9 and 360 respectively. if one number is 45. writing the other number Related: Facts that Matter, Real Numbers - Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the HCF and LCM of two number s are 9 and 360 respectively. if one number is 45. writing the other number Related: Facts that Matter, Real Numbers - Mathematics for Class 10th.
the HCF and LCM of two number s are 9 and 360 respectively. if one number is 45. writing the other number Related: Facts that Matter, Real Numbers - Mathematics for Class 10th for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about the HCF and LCM of two number s are 9 and 360 respectively. if one number is 45. writing the other number Related: Facts that Matter, Real Numbers - Mathematics for Class 10th covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the HCF and LCM of two number s are 9 and 360 respectively. if one number is 45. writing the other number Related: Facts that Matter, Real Numbers - Mathematics for Class 10th.
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