Question

If a = $2^3\times 3^3\times 7^2$and $b=2^2\times 3^2\times 5^3,$ which is true?

• A. $HCF=2^2\times 3^2;LCM=2^3\times 3^3\times 5^3\times 7^2$
  
• B. $HCF=2^3\times 3^2;LCM=2^3\times 3^2\times 5^2\times 7^3$
  
• C. $HCF=2^3\times 3^2;LCM=2^3\times 3^2\times 5^3\times 7^3$
  
• D. $LCM=2^2\times 3^2;HCF=2^3\times 3^3\times 5^3\times 7^2$

Answer 1

The correct option is A $HCF=2^2\times 3^2;LCM=2^3\times 3^3\times 5^3\times 7^2$


HCF = Product of the smallest powers of each common prime factor in the numbers.
= p min (l,x) $\times$ q min (m,y) $\times$ r min (n,z)
where, min (l,x) is the value which is minimum between l and x.
LCM = Product of the largest powers of each common prime factor in the numbers.
= p max (l,x) $\times$q max (m,y) $\times$r max (n,z)
where, max (l,x) is the value which is maximum between l and x.
The common prime factors of a and b are 2 and 3.
$Thus,HCF=2min(3,2)\times 3min(3,2)=2^2\times 3^2.$
All the prime factors of a and b are 2,3,5 and 7.
$Thus,LCM=2max(3,2)\times 3max(3,2)\times 5max(0,3)\times 7max(2,0)=2^3\times 3^3\times 5^3\times 7^2$