Question

State fundamental theorem of arithmetic. Is it possible that HCF and LCM of two numbers be 24 and 540 respectively? Justify your answer

Answer 1

Let 2 numbers be X and Y . 
HCF is a factor of X , so X = 24x . x is a positive integer . 
HCF is a factor of Y , so Y = 24y . y ia a positive integer . 
If x and y have a common factor c , then HCF becomes 24c . Therefore x and y are coprime . 
So LCM of x and y is xy , therefore LCM of X and Y is 24*(xy) . So 
24*(xy) = 540 
xy = 540/24 = 22.5 
22.5 is not an integer , so it is impossible that HCF of X and Y is 24 and LCM of X and Y is 540 .