Question

LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 80, then what is the other number?

Answer 1

Answer:

∴LCM =14 x 40=560.

∴Other number =HCF x LCM

Given number=40⋅560280

                       =80.

Step-by-step explanation:

Hii friends,

Let the HCF of two numbers is X.

Then,

LCM of two numbers= 14X.

According to question,

14X + X = 600

15X = 600

X = 600/15

X = 40

HCF of two numbers = X = 40

LCM of two numbers = 14X = 14 × 40 = 560

One Number = 280

We know that,

One Number × Other Number = HCF × LCM

280 × Other Number = 40 × 560

Other Number = 40 × 560 / 280

Other Number = 80

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Answer 2

Answer- The above question is from the chapter 'Real Numbers'.

Concept used: For two numbers a and b,

LCM (a, b)× HCF (a, b) = Product of a and b

Given question: LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 80, then what is the other number?

Solution: Let HCF of two numbers be x.

LCM = 14x

Also, LCM + HCF = 600

14x + x = 600

15x = 600

x = 600/15 = 40

⇒ HCF = 40

LCM = 14 × 40 = 560

We know that,  LCM (a, b)× HCF (a, b) = Product of a and b.

Let a = 80.

b = ?

560 × 40 = 80 × b

b = 560/2

b = 280

∴ The other number is 280.