Question

if 30 x square y 4 is LCM of expression 6 x square by 4 and 10 x y squared then their HCF will be

Answer 1

let x=khx=kh and y=lhy=lh. By definition, kk and ll are mutually prime. Then, x+y=(k+l)hx+y=(k+l)h and |x−y|=|k−l|h|x−y|=|k−l|h. Therefore, their highest common factor is hhtimes the highest common factor of k+lk+land |k−l||k−l|. This could be anything. For example, if kk and ll are prime numbers >2>2, then 22 will always be a common factor of k+lk+l and |k−l||k−l|.
CASE 1: 
If the two numbers have common factor=1, (co-primes) 
Then HCF of x+y and |x-y| will be unpredictable 
Examples: 
a) Let the two numbers be 7, 9
x+y=16, x-y=2
HCF= 2
b) Let the two numbers be 3,4 
x+y=7, |x-y|=1
HCF=1

CASE 2:
If the two numbers have a common factor other than 1 (SAY h) 
Then the HCF of x+y and |x-y| will be h itself. (PARDON ME FOR THE EXPLANATION) 
Examples:
a) let the two numbers be 4, 6 HCF=2
now x+y=10, x-y=2
HCF of these numbers =2 (Same) 
b) let the two numbers be 24, 60 HCF=12
now x+y=84, x-y=36
HCF of these numbers =12