Question

The LCM and HCF of two numbers are 924 and 4 respectively.If the sum of the numbers is 128 , then the difference is?
Can anyone explain ​

Answer 1

Answer: ±40

Step-by-step explanation:

We have,

Let the two numbers be 'a' and 'b'.

We have,

LCM(a,b)=924

HCF(a,b)=4

We know that, by Euclid's Formula

$HCF(a,b)*LCM(a,b)=a*b\\ \\924*4=a*b\\ \\a*b=3696$

Also, given that

a+b=128

Now, we know that

$(a-b)^2=(a+b)^2-4ab\\ \\=128^2-4*3696=1600\\ \\=>(a-b)^2=1600\\ \\=>(a-b) =\pm40$

Hence,

Our required answer is ±40.

If a>b,

then a-b = 40

a+b=128

=> 2a=168

=> a=84 , b = 44

Answer 2

Answer:

The difference between the two numbers is = 40