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The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.?
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The LCM and HCF of two numbers are 455, and 13 respectively. If one of...
Understanding LCM and HCF
The relationship between the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers can be expressed as:
- LCM × HCF = Product of the two numbers
Given:
- LCM = 455
- HCF = 13
Calculating the Product of the Numbers
Using the formula:
- Product = 455 × 13 = 5915
Finding the Two Numbers
Let the two numbers be x and y. According to the property of HCF, we can write:
- x = 13a
- y = 13b
where a and b are coprime integers. This means:
- x × y = (13a) × (13b) = 169ab
Equating the two products:
- 169ab = 5915
- ab = 5915 / 169 = 35
Finding Factor Pairs of 35
The factor pairs of 35 are:
- (1, 35)
- (5, 7)
Thus, our pairs (a, b) can be:
- (1, 35) leading to numbers 13 and 455
- (5, 7) leading to numbers 65 and 91
Identifying the Middle Number
We need to find which of the numbers lies between 75 and 125:
- From the pairs, the possible candidates are 91 and 65.
Since 91 is the only number that fits within the range of 75 and 125, we highlight it as the answer.
Final Answer
- The number located in the middle of 75 and 125 is: 91.
The relationship between the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers can be expressed as:
- LCM × HCF = Product of the two numbers
Given:
- LCM = 455
- HCF = 13
Calculating the Product of the Numbers
Using the formula:
- Product = 455 × 13 = 5915
Finding the Two Numbers
Let the two numbers be x and y. According to the property of HCF, we can write:
- x = 13a
- y = 13b
where a and b are coprime integers. This means:
- x × y = (13a) × (13b) = 169ab
Equating the two products:
- 169ab = 5915
- ab = 5915 / 169 = 35
Finding Factor Pairs of 35
The factor pairs of 35 are:
- (1, 35)
- (5, 7)
Thus, our pairs (a, b) can be:
- (1, 35) leading to numbers 13 and 455
- (5, 7) leading to numbers 65 and 91
Identifying the Middle Number
We need to find which of the numbers lies between 75 and 125:
- From the pairs, the possible candidates are 91 and 65.
Since 91 is the only number that fits within the range of 75 and 125, we highlight it as the answer.
Final Answer
- The number located in the middle of 75 and 125 is: 91.
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The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.?
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The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.?.
The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The LCM and HCF of two numbers are 455, and 13 respectively. If one of them is located in the middle of 75 and 125, that number is options are 78, 91, 104, or 117.?.
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