Question

The lcm of two number S is 14 times their hcf the sum of lcm and hcm is 600 if one number is 280 then find the other number

Answer 1

HCF X LCM = A x B
let the numbers are A and B
let LCM be x and HCF be y.
x=14y
x+y= 600
$x - 14y = 0 \\ x + y = 600 \\ subtract \: both \: eq \\ - 15y = - 600 \\ y = \frac{600}{15} \\ y = 40 \\ x + 40 = 600 \\ x = 560$

so LCM is 560, HCF is 40
from the formula
$40 \times 560 = 280 \times b \\ b = \frac{560 \times 40}{280} \\ b = 80$
so the other number is 80.

Answer 2

Answer:let H.C.F Be x

according to the question

                L.C.M=14x

  The sum of L.c.m and H.c.f is 600

    ⇒x+14x=600

     ⇒15x=600

    ⇒x=40

∴h.c.f=40 --------------------------1

     L.C.M=14×40=560 ---------------------------2

WE KNOW THAT LCM ×HCF =PRODUCT OF TWO NUMBERS

ONE NUMBER IS 280          (given)

let other number be Y

                  560×40=280×Y

                 ⇒Y=80

    ∴OTHER NUMBER IS 80