The LCM of $$8^2×6^3$$​ and $$4^6×9^3$$​ is:

Correct option is C

Given:

We are to find the LCM of:

​$$8^2 \times 6^3$$​​

​$$4^6 \times 9^3$$​​

Solution:
Prime factorizations:

​$$8 = 2^3$$​

​$$8^2 = 2^6$$​​

​$$6 = 2 \times 3$$​

​$$6^3 = 2^3 \times 3^3$$​​
$$8^2 \times 6^3 = 2^6 \times 2^3 \times 3^3 = 2^9 \times 3^3$$​​

​$$4 = 2^2$$​

​$$4^6 = 2^{12}$$​​

​$$9 = 3^2$$​

​$$9^3 = 3^6$$​​
So, $$4^6 \times 9^3 = 2^{12} \times 3^6$$​​

Now,

​$$\text{LCM} = \text{Highest powers of all primes} = 2^{\max(9,12)} \times 3^{\max(3,6)} = 2^{12} \times 3^6$$​