Question

If $a=2^3\times 3^3\times 7^2\text{and}b=2^2\times 3^2\times 5^3,$ 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

Answer: (A)

Given:
$a=2^3\times 3^3\times 7^2$

$b=2^2\times 3^2\times 5^3,$

We know that in prime factorization,
$HCF=$ Product of the least powers of each common prime factor.

Here, common prime factors are $2$ and $3$.

$\Rightarrow HCF=2^{min(3,2)}\times 3^{min(3,2)}$

$\Rightarrow HCF=2^2\times 3^2$ ---(1)

Again in prime factorization
$LCM=$ Product of the greatest powers of each prime factor and other prime factors.
$\Rightarrow LCM=2^{max(2,3)}\times 3^{max(2,3)}\times 7^2\times 5^3$

$\Rightarrow LCM=2^3\times 3^3\times 5^3\times 7^2$ ---(2)

From (1) and (2) Option $\left(A\right)$ is True. .