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The lcm of 2 coprime numbers is 176. if one number is 16, find the other number?
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The lcm of 2 coprime numbers is 176. if one number is 16, find the oth...
Understanding the Problem
To find the other number when given that the least common multiple (LCM) of two coprime numbers is 176 and one number is 16, we can use the properties of coprime numbers.
Properties of Coprime Numbers
- Coprime Definition: Two numbers are coprime if their greatest common divisor (GCD) is 1.
- LCM and GCD Relationship: For any two numbers a and b, the relationship is given by:
LCM(a, b) = (a * b) / GCD(a, b)
Since the numbers are coprime, the GCD of 16 and the unknown number (let's call it x) is 1.
Calculating the Other Number
- Using the LCM Formula:
- We know LCM(16, x) = (16 * x) / GCD(16, x)
- Since GCD(16, x) = 1 (because they are coprime), the formula simplifies to:
LCM(16, x) = 16 * x
- Setting Up the Equation:
- Given LCM(16, x) = 176, we have:
16 * x = 176
- Solving for x:
- To find x, divide both sides by 16:
x = 176 / 16
x = 11
Final Result
- The other number is 11.
This can be verified by checking that the LCM of 16 and 11 is indeed 176, confirming the calculations.
To find the other number when given that the least common multiple (LCM) of two coprime numbers is 176 and one number is 16, we can use the properties of coprime numbers.
Properties of Coprime Numbers
- Coprime Definition: Two numbers are coprime if their greatest common divisor (GCD) is 1.
- LCM and GCD Relationship: For any two numbers a and b, the relationship is given by:
LCM(a, b) = (a * b) / GCD(a, b)
Since the numbers are coprime, the GCD of 16 and the unknown number (let's call it x) is 1.
Calculating the Other Number
- Using the LCM Formula:
- We know LCM(16, x) = (16 * x) / GCD(16, x)
- Since GCD(16, x) = 1 (because they are coprime), the formula simplifies to:
LCM(16, x) = 16 * x
- Setting Up the Equation:
- Given LCM(16, x) = 176, we have:
16 * x = 176
- Solving for x:
- To find x, divide both sides by 16:
x = 176 / 16
x = 11
Final Result
- The other number is 11.
This can be verified by checking that the LCM of 16 and 11 is indeed 176, confirming the calculations.
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The lcm of 2 coprime numbers is 176. if one number is 16, find the other number?
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The lcm of 2 coprime numbers is 176. if one number is 16, find the other number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The lcm of 2 coprime numbers is 176. if one number is 16, find the other number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lcm of 2 coprime numbers is 176. if one number is 16, find the other number?.
The lcm of 2 coprime numbers is 176. if one number is 16, find the other number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The lcm of 2 coprime numbers is 176. if one number is 16, find the other number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lcm of 2 coprime numbers is 176. if one number is 16, find the other number?.
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