__maths__>__Divisibility in Whole Numbers__>__Least 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`".

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`

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