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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsDivisibility in Whole NumbersLeast Common Multiple

Relation between two numbers, their LCM and HCF

This page provides a brief overview of the relationship, product of numbers equals product of their LCM and HCF.



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What is the HCF of `36` and `48`?

  • `36`
  • `12`
  • `12`

The answer is "`12`".
hcf

What is the LCM of `36` and `48`?

  • `48`
  • `144`
  • `144`

The answer is "`144`".
lcm using factorization method

Consider the example : finding HCF of two numbers.hcf using factorization method Which of the following is a description of HCF?

  • product of common prime-factors
  • product of common prime-factors
  • product of common and non-common prime-factors

The answer is "product of common prime-factors"

Consider the example : finding LCM of two numbers.lcm using factorization method Which of the following is a description of LCM?

  • product of common prime-factors
  • product of common and non-common prime-factors
  • product of common and non-common prime-factors

The answer is "product of common and non-common prime-factors"

Consider two numbers with HCF `n`. The numbers can be given in the form `nxxp` and `nxxq`.

For example, HCF `36` and `48` is `12`.
And `36=12xx3` and `48=12xx4`.
In this example `n=12`, `p=3` and `q=4`.

The `p` and `q` are derived from the non-common prime factors of the two numbers. What is the `LCM` of the two numbers `nxxp` and `nxxq`?

  • LCM cannot be found using the given information
  • `nxxpxxq`
  • `nxxpxxq`

The answer is "`nxxpxxq`"

Given two numbers `nxxp` and `nxxq` where `n` is the HCF and `nxxpxxq` is the LCM.

Is there a relation between the two numbers, the HCF and the LCM?

  • product of the numbers equal product of LCM and HCF
  • `(nxxp)xx(nxxq) = text( HCF ) xx text( LCM )`
  • both the above
  • both the above

The answer is "both the above".

LCM HCF Product Property : Product of LCM and HCF equals product of the numbers.

Given LCM `440` and HCF `22`. One number is `88` what is the other number?

  • `110`
  • `110`
  • `220`

The answer is "`110`".

As per the LCM HCF Product Property
`440 xx 22 = 88 xx text( number )`

number = `440xx22 -:88`
`=110`

                            
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