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Class 10MathematicsReal NumbersHCF and LCM using prime factorisationHardLevel 12
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If (54), (90), and (126) are to be divided by the same greatest possible number, what is that number?

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Answer and explanation

Correct answer: (18)

Step 1: The greatest common divisor is the HCF. Step 2: (54=2\times3^3), (90=2\times3^2\times5), and (126=2\times3^2\times7), so HCF (=2\times3^2=18). Step 3: Take the smallest powers common to all numbers.

Related tags

Real-NumbersHcfCommon-Divisor

Frequently asked questions

What is the correct answer to this question?

(18)

Why is this the correct answer?

Step 1: The greatest common divisor is the HCF. Step 2: (54=2\times3^3), (90=2\times3^2\times5), and (126=2\times3^2\times7), so HCF (=2\times3^2=18). Step 3: Take the smallest powers common to all numbers.

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?
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  5. 5What is the LCM of (40) and (60)?
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  7. 7What will be the LCM of (45) and (75)?
  8. 8Which is the HCF of (32) and (48)?
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