Question

the sum of two numbers is 2000 and their l.c.m 21879.the two numbers are

Answer 1

Let the numbers be x and (2000 - x).

Then, their L.C.M. = x (2000 - x).

So, x (2000 - x) = 21879

<=> x2 - 2000x + 21879 = 0.

<=> (x - 1989) (x - 11) = 0,

<=> x = 1989 or x = 11.

Hence, the numbers are 1989 and 11.

Answer 2

The numbers are 1989 and 11

Given :

The sum of two numbers is 2000 and their LCM is 21879

To find :

The numbers

Solution :

Step 1 of 2 :

Form the equation to find the numbers

Here it is given that the sum of two numbers is 2000

Let the numbers be x and (2000 - x)

∴ LCM = x(2000 - x)

Now it is given that their LCM is 21879

∴ x(2000 - x) = 21879

Step 2 of 2 :

Find the numbers

x(2000 - x) = 21879

⇒ x² - 2000x + 21879 = 0

⇒ x² - (1989 + 11)x + 21879 = 0

⇒ x² - 1989x - 11x + 21879 = 0

⇒ x(x - 1989) - 11(x - 1989) = 0

⇒ (x - 1989) (x - 11) = 0

Now ,

x - 1989 = 0 gives x = 1989

x - 11 = 0 gives x = 11

Hence the numbers are 1989 and 11

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