Question

The lcm of two numbers is 14 times their hcf. The sum of lcm and hcf is 600. If one of the number is 280 then the other number is-

Answer 1

Answer:

Explanation:

GIVEN: HCF+LCM= 600, ONE NUMBER= 280

Let the HCF= X

LCM= 14X

HCF+LCM= 600

X+ 14X=600

15X= 600

X= 600/15

X= 40

HCF= 40

LCM = 14X= 14× 40= 560

HCF×LCM= 1ST NUMBER × 2ND NUMBER

40× 560= 280× 2ND NUMBER

2ND NUMBER= (40×560) /280

2ND NUMBER= 40×2

2ND NUMBER= 80

Hope this will help you....

Answer 2

Answer:

The other number is 80

Explanation:

Let the two number be x and y.

Their LCM be L and their HCF be H

LCM of x and y = 14 * H  ⇒ L = 14H    .....(i)

L  + H  = 600 ⇒ L = 600 - H     .........(ii)

Eqauting (i) and (ii), we get

      14H = 600 - H

14H + H = 600

      15H = 600

          H = 40

Using H =40 in (i), we get

L = 14 * 40

L= 560

Also, Let x = 280

Product of two numbers =  H.C.F. ×  L.C.M.

                           x * y        = H * L

                             280 * y  =  40 * 560

                                       y  =  40 * 560 / 280

                                      y  =  80