Find gcd(92928,123552) and lcm(92928, 123552), and verify that gcd(92928, 123552) · lcm(92928, 123552) = 92928 · 123552. [Hint: First find the prime factorizations of 92928 and 123552.]

Solution:-Step1Given thatWe have to find gcd(92928,123552) and lcm(92928, 123552), and verify that gcd(92928, 123552) · lcm(92928, 123552) = 92928 · 123552. Step2We havegcd(92928,123552)Prime factorization of 9292892928= =Prime factorization of 123552123552= = Step3gcd(92928,123552)= gcd(,) =Therefore, gcd(92928,123552) is .Step4 lcm(92928, 123552)=lcm(,) = =Therefore, lcm(92928, 123552) is Step5gcd(92928, 123552) · lcm(92928, 123552) = 92928 · 123552. Here LHS(Left hand side)=gcd(92928, 123552) · lcm(92928, 123552) RHS(right hand side)= 92928 · 123552LHS=gcd(92928, 123552) · lcm(92928, 123552) = = =(92928 123552) = RHSTherefore, LHS=RHSHence, gcd(92928, 123552) · lcm(92928, 123552) = 92928 · 123552.