Class 10 Exam > Class 10 Questions > The HCF of 2472,1284 and a third number n is ...
Start Learning for Free
The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is?
Most Upvoted Answer
The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²...
Community Answer
The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²...
To find the third number, we need to first find the prime factors of the given LCM and the given HCF.
Given LCM: 2² × 3² × 5 × 10³ × 107
Given HCF: 12
Finding the Prime Factors of LCM:
1. The prime factors of 2² are 2 and 2.
2. The prime factors of 3² are 3 and 3.
3. The prime factors of 5 are 5.
4. The prime factors of 10³ are 2, 2, 2, 5, and 5.
5. The prime factors of 107 are 107.
Prime Factors of LCM: 2, 2, 3, 3, 5, 2, 2, 2, 5, 5, 107
Finding the Prime Factors of HCF:
1. The prime factors of 12 are 2, 2, and 3.
Prime Factors of HCF: 2, 2, 3
To find the third number, we need to cancel out the common prime factors between the LCM and HCF, leaving only the unique prime factors.
Cancelling out Common Prime Factors:
1. Cancel out two 2's from the LCM and HCF.
2. Cancel out one 3 from the LCM and HCF.
Remaining Prime Factors: 5, 2, 5, 107
The third number, n, is the product of the remaining prime factors: 5 × 2 × 5 × 107 = 5² × 2 × 107 = 5350.
Therefore, the number n is 5350.
Given LCM: 2² × 3² × 5 × 10³ × 107
Given HCF: 12
Finding the Prime Factors of LCM:
1. The prime factors of 2² are 2 and 2.
2. The prime factors of 3² are 3 and 3.
3. The prime factors of 5 are 5.
4. The prime factors of 10³ are 2, 2, 2, 5, and 5.
5. The prime factors of 107 are 107.
Prime Factors of LCM: 2, 2, 3, 3, 5, 2, 2, 2, 5, 5, 107
Finding the Prime Factors of HCF:
1. The prime factors of 12 are 2, 2, and 3.
Prime Factors of HCF: 2, 2, 3
To find the third number, we need to cancel out the common prime factors between the LCM and HCF, leaving only the unique prime factors.
Cancelling out Common Prime Factors:
1. Cancel out two 2's from the LCM and HCF.
2. Cancel out one 3 from the LCM and HCF.
Remaining Prime Factors: 5, 2, 5, 107
The third number, n, is the product of the remaining prime factors: 5 × 2 × 5 × 107 = 5² × 2 × 107 = 5350.
Therefore, the number n is 5350.
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
The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is?
Question Description
The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? 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 of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is?.
The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? 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 of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is?.
Solutions for The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? 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 The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? defined & explained in the simplest way possible. Besides giving the explanation of
The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is?, a detailed solution for The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? has been provided alongside types of The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? theory, EduRev gives you an
ample number of questions to practice The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²×5×10³×107, then the number n is? 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