Question

the LCM of 2 numbers is 14 times their HCF. the sum of LCM and HCF is 600. if one number is 280. find the other no.

Answer 1

let us think the other number be x
given,lcm(280,x)_=14×hcf(280,x)
   lcm(280,x)+hcf(280,x)=600
⇒14×hcf(280,x)+hcf(280,x)=600
⇒15×hcf(280,x)=600
⇒hcf(280,x)=40
lcm(280,x)=14×40=560
we know that , lcm×hcf=280× x
                      ⇒560×40=280× x
                       ⇒x=560×40/280
                        ⇒x=2×40
                         ⇒x=80
∴other number=80

Answer 2

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....