Question

the LCM of 2 numbers is 14 times their HCF . the sum of LCM and HCF is 600 . if one number is 280 , then find the other number​

Answer 1

Answer:

80

Step-by-step explanation:

Let the other number be ′x′

 Given:LCM+HCF=600

⇒14HCF+HCF=600

⇒15HCF=600

⇒HCF=40

⇒LCM=14×40=560

we know that, HCFxLCM=Product of 2 numbers

=>40×560 = 280×x

=>X=(40x560)÷280

⇒x=80

hence the other number is 80.

Answer 2

Step-by-step explanation:

Given:-

The LCM of 2 numbers is 14 times their HCF .

The sum of LCM and HCF is 600 .

One number is 280 .

To find:-

Find the other number ?

Solution:-

Let the other number be b

Given that

One number = (a) = 280

The LCM of two numbers = 14 times thier HCF

=> LCM = 14× HCF

=> L = 14 H ------------(1)

and

The sum of the LCM and the HCF = 600

=> LCM + HCF = 600

=> L+H = 600 ----------(2)

On Substituting the value of L in (2)

=> 14H + H = 600

=> 15 H = 600

=> H = 600/15

=> H = 40

HCF = 40

On Substituting the value of H in (1)

=> L = 14×40

=> L = 560

LCM = 560

Now , we Know that

LCM × HCF = Product of two numbers

=> L× H = a×b

=> b = (L×H)/a

=> b = (560×40)/280

=> b = 2×40

=> b = 80

Answer:-

The other number for the given problem is 80

Used formulae:-

• LCM × HCF = Product of two numbers