Question

If two natural numbers are multiplied, they give a number which is their LCM.

Write two conclusive statements from this

Subject :- Maths

Answer 1

Hey there!

Let the numbers be a, b.

Given that,

Product of numbers = LCM.

a * b = LCM.

Now, Let this be the equation of reference.

We know that,

Product of numbers = LCM * HCF

So, a * b = LCM * HCF

a * b = a * b * HCF from equation of reference

HCF = 1 .

So , One conclusive statement is the HCF of numbers is 1 .

We know that, When two numbers have HCF or GCD = 1 , they are co-primes .

So, Other conclusive statement is They are co primes.

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Now, If two numbers are multiplied, they give result as LCM ,

From this statement,

The following conclusive statements can be made :

1) The numbers are Co-primes.

2) The number have 1 as Highest common factor

Answer 2

let two number => X and Y ,

now , if we multiply , we get


X*Y = >. their HCF ( GCD ) * their LCM .



now , look the example =>



5* 4 => their { HCF } * their { LCM }


20 = 20 * 1


=> now , if we require to find , LCM

we can go through this mathod => X* Y / HCF => LCM


theirfor ,. 20 /1 => 20 .




here from EXAMPLE we get => X*Y => LCM


i.e => 20 =20 .



hence , the LCM = Product of two numbers / HCF ..


or simply , LCM => Product of two numbers





hope now it's clear !!!



thanks , for nice question !!