Question

The LCM of two numbers is 14times their HCF.The sum of LCM and HCF is 600.If one number is 280,then find the other number.

Answer 1

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

Answer 2

Let the HCF be x.
Then, LCM =14x.
Given that ,x +14x= 600.
15x=600
x=40.
Given One no.=280
Since LCM×HCF=Product of 2 numbers.
560×40=280×2nd number
22400/280=2nd number.
2nd number =80.

You can assume 2nd number as 'a'.

Hope it helped!...