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The smallest number by which 5400 must be multiplied so that it become a perfect cube, is
- a)2
- b)10
- c)5
- d)3
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The smallest number by which 5400 must be multiplied so that it become...
Find prime factors of 5400
5400=2x3x3x3x2x2x5x5
If we group them in the group of 3
5400=(2x2x2)x(3x3x3)x5x5
Here to make group of 3 for 5
We have to multiply 5400 by 5.
Answer is 5
Most Upvoted Answer
The smallest number by which 5400 must be multiplied so that it become...
Understanding Perfect Cubes
To make a number a perfect cube, all the prime factors in its prime factorization must have exponents that are multiples of 3.
Prime Factorization of 5400
1. Start by breaking down 5400 into its prime factors:
- 5400 = 54 × 100
- 54 = 2 × 27 = 2 × 3^3
- 100 = 10^2 = 2^2 × 5^2
- Therefore, 5400 = 2^3 × 3^3 × 5^2
Analyzing Exponents
2. The prime factorization of 5400 is:
- 2^3
- 3^3
- 5^2
3. Now, check the exponents:
- For 2: exponent is 3 (already a multiple of 3)
- For 3: exponent is 3 (already a multiple of 3)
- For 5: exponent is 2 (not a multiple of 3)
Finding the Smallest Multiplier
4. To convert the exponent of 5 from 2 to the next multiple of 3:
- The next multiple of 3 is 3.
- Hence, we need to increase the exponent of 5 by 1 (from 2 to 3).
5. Therefore, we must multiply 5400 by 5^1, which equals 5.
Conclusion
Thus, the smallest number by which 5400 must be multiplied to become a perfect cube is 5.
Correct answer: option 'C'.
To make a number a perfect cube, all the prime factors in its prime factorization must have exponents that are multiples of 3.
Prime Factorization of 5400
1. Start by breaking down 5400 into its prime factors:
- 5400 = 54 × 100
- 54 = 2 × 27 = 2 × 3^3
- 100 = 10^2 = 2^2 × 5^2
- Therefore, 5400 = 2^3 × 3^3 × 5^2
Analyzing Exponents
2. The prime factorization of 5400 is:
- 2^3
- 3^3
- 5^2
3. Now, check the exponents:
- For 2: exponent is 3 (already a multiple of 3)
- For 3: exponent is 3 (already a multiple of 3)
- For 5: exponent is 2 (not a multiple of 3)
Finding the Smallest Multiplier
4. To convert the exponent of 5 from 2 to the next multiple of 3:
- The next multiple of 3 is 3.
- Hence, we need to increase the exponent of 5 by 1 (from 2 to 3).
5. Therefore, we must multiply 5400 by 5^1, which equals 5.
Conclusion
Thus, the smallest number by which 5400 must be multiplied to become a perfect cube is 5.
Correct answer: option 'C'.
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The smallest number by which 5400 must be multiplied so that it become a perfect cube, isa)2b)10c)5d)3Correct answer is option 'C'. Can you explain this answer?
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The smallest number by which 5400 must be multiplied so that it become a perfect cube, isa)2b)10c)5d)3Correct answer is option 'C'. Can you explain this answer? for LR 2025 is part of LR preparation. The Question and answers have been prepared according to the LR exam syllabus. Information about The smallest number by which 5400 must be multiplied so that it become a perfect cube, isa)2b)10c)5d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for LR 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest number by which 5400 must be multiplied so that it become a perfect cube, isa)2b)10c)5d)3Correct answer is option 'C'. Can you explain this answer?.
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