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Class 10MathematicsReal NumbersFundamental Theorem of ArithmeticHardLevel 5
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If (a=2^4\times3^3\times13) and (b=2^2\times3\times5\times13^2), what is the LCM of (a) and (b)?

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Answer and explanation

Correct answer: 365040

Step 1: For LCM, take the highest powers of all prime factors. Step 2: The highest powers are (2^4), (3^3), (5), and (13^2). Step 3: (16\times27\times5\times169=365040), so the answer is 365040.

Related tags

LcmPrime-FactorisationHard

Frequently asked questions

What is the correct answer to this question?

365040

Why is this the correct answer?

Step 1: For LCM, take the highest powers of all prime factors. Step 2: The highest powers are (2^4), (3^3), (5), and (13^2). Step 3: (16\times27\times5\times169=365040), so the answer is 365040.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Fundamental Theorem of Arithmetic.

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  1. 1According to the Fundamental Theorem of Arithmetic, every composite number can be written in which form?
  2. 2What is the prime factorisation of 36?
  3. 3What is the correct prime factorisation of 60?
  4. 4What does uniqueness mean in the Fundamental Theorem of Arithmetic?
  5. 5In the prime factorisation of 84, what is the power of 2?
  6. 6The number (2^3\times3^2) is equal to which number?
  7. 7Which is the prime factorisation of 45?
  8. 8Which of the following numbers is prime?
  9. 9Which of the following numbers is composite?
  10. 10What is the prime factorisation of 90?
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