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Class 10MathematicsReal NumbersHCF and LCM using prime factorisationExpertLevel 10
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What is the smallest number exactly divisible by (64), (72), and (125)?

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Answer and explanation

Correct answer: (72000)

Step 1: The smallest number exactly divisible by all is the LCM. Step 2: (64=2^6), (72=2^3\times3^2), and (125=5^3), so LCM (=2^6\times3^2\times5^3=72000). Step 3: Keeping the highest powers correctly gives the right answer.

Related tags

Real-NumbersLcmDivisibility

Frequently asked questions

What is the correct answer to this question?

(72000)

Why is this the correct answer?

Step 1: The smallest number exactly divisible by all is the LCM. Step 2: (64=2^6), (72=2^3\times3^2), and (125=5^3), so LCM (=2^6\times3^2\times5^3=72000). Step 3: Keeping the highest powers correctly gives the right answer.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: HCF and LCM using prime factorisation.

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  1. 1If the product of two numbers is 3780 and their LCM is 315, what is their HCF?
  2. 2What is the HCF of (18) and (24) using prime factorisation?
  3. 3What is the LCM of (18) and (24) using prime factorisation?
  4. 4What is the HCF of (40) and (60)?
  5. 5What is the LCM of (40) and (60)?
  6. 6What will be the HCF of (45) and (75)?
  7. 7What will be the LCM of (45) and (75)?
  8. 8Which is the HCF of (32) and (48)?
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