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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?
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The HCF of 2472,1284 and a third number n is 12. If their LCM is 2²×3²...
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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.
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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 2025 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 2025 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 2025 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 2025 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?.
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