Question

The LCM of a number with 10000 is 20000. Find the minimum value of that number?

Answer 1

The minimum value of second number is 2.

Step-by-step explanation:

In the given question,

LCM of 10000 and x =20000

LCM(Least Common Multiple) is the multiple that is smallest and common in all the given numbers or the smallest number that is the multiplier of all these numbers.

For e.g LCM of 20 and 25 is 100.

i.e Since,both the numbers 20 and 25 are multiple of 100.

Hence, 100 is the LCM.

For a number 10000 and x,LCM is 20000

Also,$LCM\times HCF = Product\ of\ two\ numbers$

     $20000\times HCF = 10000\times x$

       ⇒$HCF = \frac{10000x}{20000}$

                   =$\frac{x}{2}$

⇒$10000 = \frac{x}{2}\times a$

$a = \frac{20000}{x}$

On solving

$\frac{x}{2}\times 20000 = \frac{20000}{x}\times x$

x=2

So,the minimum value of that number is 2.