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
