Smallest 4692

A. Find the largest natural number by which the numbers 54 and 72 can be divided (120, 60, and 42)
B. Find the smallest natural number that can be divided by each of the numbers 36 and 48 (24,18 and 16)

Correct answer:

a =  18
b =  144

Step-by-step explanation:

$$\begin{gathered} 54=2\cdot 3^3 \\ 72=2^3\cdot 3^2 \\ \text{GCD}(54,72)=2\cdot 3^2=18 \\ a=GCD(54,72)=18 \end{gathered}$$

$$\begin{gathered} 36=2^2\cdot 3^2 \\ 48=2^4\cdot 3 \\ LCM(36,48)=2^4\cdot 3^2=144 \\ b=LCM(36,48)=144 \end{gathered}$$

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