Answer
GCD is \[24\] and LCM is\[144\].
Work Step by Step
Write 48 and 72 in terms of prime factors as follows:
\[\begin{align}
& 48=2\times 2\times 2\times 2\times 3 \\
& 72=2\times 2\times 2\times 3\times 3 \\
\end{align}\]
Further express the factors in terms of exponents:
\[\begin{align}
& 48={{2}^{4}}\times 3 \\
& 72={{2}^{3}}\times {{3}^{2}} \\
\end{align}\]
Now, for GCD select each prime factor with the smaller exponent that is common to each of the prime factorization:
\[\begin{align}
& \text{GCD}={{2}^{3}}\times 3 \\
& =8\times 3 \\
& =24
\end{align}\]
Now, for LCM, select every prime factor that occurs, raised to the greater exponent in these prime factorizations:
\[\begin{align}
& \text{LCM}={{2}^{4}}\times {{3}^{2}} \\
& =16\times 9 \\
& =144
\end{align}\]
Hence, the GCD is \[24\] and LCM is\[144\].
