Class 10 Exam > Class 10 Questions > Assertion : The HCF of two numbers is 5 and t...
Start Learning for Free
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?
Most Upvoted Answer
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.
Community Answer
Assertion : The HCF of two numbers is 5 and their product is 150, then...
True
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup