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The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x 32 x 5 x 103 x 107, then the number N is :

  • a)
    22 x 32 x 7

  • b)
    22 x 33 x 103

  • c)
    22 x 32 x 5

  • d)
    24 x 32 x 11

Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x...
Given that, LCM (2472, 1284, and n) is 2× 3× 5 × 103 × 107


Let us express the numbers 2472, and 1284 as a product of prime numbers.


2472 = 2 × 2 × 2 × 3 × 103  (23 × 3 × 103)


1284 = 2 × 2 × 3 × 107 (2× 3 × 107)


HCF (2472, 1284)=  2 × 2 × 3 (2× 3)


'n' should also have one of the factors as HCF, and another factor as the missing element of other numbers from the LCM (i.e., 3 × 5)


Therefore,


n =  22 × 3 × (3 × 5)


n = 22 × 32 × 5


n = 4 × 9 × 5


n = 180


Therefore, if the HCF of 2472 and 1284 and a third number 'n' is 12 and if their LCM is 23 × 3× 5 × 103 × 107, then the number 'n' is 180 (22 × 32 × 5)
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Most Upvoted Answer
The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x...
Something is wrong in this question ,
because see,
2472=2³×3×103,
1284=2²×3×107,
N=2²×3×z,
HCF×LCM=2472×1284×12z,
z=15,
N=2²×3²×5
Free Test
Community Answer
The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x...
Product of the no. = 2472×1284×N
HCF=12
LCM=8×9×5×103×107
--> HCF×LCM=Product of the no.
**Now put the values nd obtain the magnitude of N**
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The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x 32 x 5 x 103 x 107, then the number N is :a)22 x 32 x 7b)22 x 33 x 103c)22 x 32 x 5d)24 x 32 x 11Correct answer is option 'C'. Can you explain this answer?
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The HCF of 2472, 1284 and a third number N is 12. If their LCM is 23 x 32 x 5 x 103 x 107, then the number N is :a)22 x 32 x 7b)22 x 33 x 103c)22 x 32 x 5d)24 x 32 x 11Correct answer is option 'C'. Can you explain this answer? 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 23 x 32 x 5 x 103 x 107, then the number N is :a)22 x 32 x 7b)22 x 33 x 103c)22 x 32 x 5d)24 x 32 x 11Correct answer is option 'C'. Can you explain this answer? 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 23 x 32 x 5 x 103 x 107, then the number N is :a)22 x 32 x 7b)22 x 33 x 103c)22 x 32 x 5d)24 x 32 x 11Correct answer is option 'C'. Can you explain this answer?.
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