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Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point?
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Assertion : The HCF of two numbers is 5 and their product is 150, then...
Assertion and Reasoning
Assertion: The HCF of two numbers is 5 and their product is 150, then their LCM is 30.
Reason: For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b.
Explanation:
To prove the assertion and reasoning statement, let's first understand the terms HCF and LCM.
HCF (Highest Common Factor) - The highest common factor or greatest common divisor (GCD) is the largest positive integer that divides two or more numbers without remainder.
LCM (Least Common Multiple) - The least common multiple or lowest common multiple (LCM) is the smallest positive integer that is divisible by two or more numbers without a remainder.
Now, let's apply the reasoning formula to the given numbers.
Given, HCF of two numbers is 5 and their product is 150.
Let's assume the two numbers as a and b.
HCF (a, b) = 5 and a x b = 150.
Using the reasoning formula, we get:
HCF (a, b) x LCM (a, b) = a x b
Substituting the given values, we get:
5 x LCM (a, b) = 150
LCM (a, b) = 150/5
LCM (a, b) = 30
Therefore, the LCM of the two numbers is 30, which proves the assertion and reasoning statement true.
Conclusion:
The assertion and reasoning statement is true, and we can say that the LCM of two numbers whose HCF is 5 and product is 150 is 30.
Assertion: The HCF of two numbers is 5 and their product is 150, then their LCM is 30.
Reason: For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b.
Explanation:
To prove the assertion and reasoning statement, let's first understand the terms HCF and LCM.
HCF (Highest Common Factor) - The highest common factor or greatest common divisor (GCD) is the largest positive integer that divides two or more numbers without remainder.
LCM (Least Common Multiple) - The least common multiple or lowest common multiple (LCM) is the smallest positive integer that is divisible by two or more numbers without a remainder.
Now, let's apply the reasoning formula to the given numbers.
Given, HCF of two numbers is 5 and their product is 150.
Let's assume the two numbers as a and b.
HCF (a, b) = 5 and a x b = 150.
Using the reasoning formula, we get:
HCF (a, b) x LCM (a, b) = a x b
Substituting the given values, we get:
5 x LCM (a, b) = 150
LCM (a, b) = 150/5
LCM (a, b) = 30
Therefore, the LCM of the two numbers is 30, which proves the assertion and reasoning statement true.
Conclusion:
The assertion and reasoning statement is true, and we can say that the LCM of two numbers whose HCF is 5 and product is 150 is 30.
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Assertion : The HCF of two numbers is 5 and their product is 150, then...
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Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point?
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Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point? 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 Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point?.
Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point? 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 Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion : The HCF of two numbers is 5 and their product is 150, then their LCM is 30 Reason : For any two positive integers a and b, HCF (a,b) X LCM (a,b) = a X b. * 1 point?.
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