Question

Hcf of two numbers is 84 and lcm is 1260 then the sum of two numbers is

Answer 1

Answer:

The sum of two numbers is 672

Step-by-step explanation:

Given as :

The HCF of two numbers = 84

The LCM of two numbers = 1260

Let The number be 84 x , 84 y

Since,

Product of numbers = products of HCF and LCM

i.e 84 x × 84 y = 84 × 1260

Or, x y = $\dfrac{1260}{84}$

So, x y = 15

Here x , y must be co-prime

co-prime of 15 = ( 1 , 15 ) , ( 3 , 5) , (5 , 3) , (15 , 1)

So, The first number = 84 x = 84 × 3 = 252

And  ,The second number =  84 y = 84 × 5 = 420

∵  The LCM of 252 , 420 = 1260

So, The two number must be 252 , 420

Or, The sum of two numbers = 252 + 420 = 672

Hence, The sum of two numbers is 672 . Answer