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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.
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.

click on the content to continue..

What is the HCF of 36 and 48?

• 36
• 12
• 12

The answer is "12".

What is the LCM of 36 and 48?

• 48
• 144
• 144

The answer is "144".

Consider the example : finding HCF of two numbers. 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. 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

slide-show version coming soon