Find gcd(92928, 123552) and lcm(92928, 123552), and verify that gcd(92928, 123552) · lcm(92928, 123552 ) = 92928 · 123552

We know that

92928> (2^8)*(3)*(11²)
123552> (2^5)*(3³)*(11)*(13)

then 
gcd> (2^5)*(3)*(11)> 1056
lcm> (2^8)*(3³)*(11²)*(13)> 10872576

step 1
find  [gcd(92928, 123552) * lcm(92928, 123552 )]
=[(2^5)*(3)*(11)]*[(2^8)*(3³)*(11²)*(13)]-> (2^13)*(3^4)*(11³)*(13)=equation 1

step 2
find [92928 * 123552]
=[(2^8)*(3)*(11²)]*[(2^5)*(3³)*(11)*(13)]
=(2^13)*(3^4)*(11³)*(13)> equation 2

I compare equation 1 with equation 2
and
equation 1=equation 2

hence
[gcd(92928, 123552)*lcm(92928, 123552)]=[92928*123552]

the answer is 
a) gcd (92928,123552) is (2^5)*(3)*(11)> 1056
b) lcm (92928,123552) is (2^8)*(3³)*(11²)*(13)> 10872576
c) [gcd(92928,123552)*lcm(92928,123552)]=[92928*123552]> verified