Question

the LCM of two number is 14 times their HCF the sum of LCM and HCF is 600 if one of number is 280 then find the other number

Answer 1

Let us denote HCF by h and LCM by l
now
given : l=14h
and we know
l*h=product of the numbers
let the other no. be X
therefore
14h*h=280*X
and given
l+h=600
15h=600
h=40
therefore
(14*40*40)280=X
=X=80
hence the other no. is 80

Answer 2

We know,
LCM X HCF = product of two numbers ( a, b)
Also, LCM * 14 = HCF.......(I)
LCM + HCF = 600.........(II)

Let, a =280

From I and II
15 LCM = 600
LCM = 40.........(III)

substituting in (II)
HCF = 560.......(IV)

Now, 40*560 = 280*b
b = 80