Practice

1. Find the GCF of 72 and 48

$$\begin{gathered} 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, \overline{)24}, 36, 72 \\ 48: 1, 2, 3, 4, 6, 8, 12, 16, \overline{)24}, 48 \\ \mathrm{GCF}\left(72, 48\right)=24 \end{gathered}$$

2. Find the LCM of 24 and 18

$$\begin{gathered} 24: 24, 48, \overline{)72}, ... \\ 18: 18, 36, 54, \overline{)72}, ... \\ \mathrm{LCM}\left(24, 18\right)=72 \end{gathered}$$

3. Find the LCM of 15 and 25

$$\begin{gathered} 15: 15, 30, 45, 60, \overline{)75}, ... \\ 25: 25, 50, \overline{)75} , ... \\ \mathrm{LCM}\left(15, 25\right)=75 \end{gathered}$$

4. Find the GCF of 18 and 30

$$\begin{gathered} 18: 1, 2, 3, \overline{)6}, 9, 18 \\ 30: 1, 2, 3, 5, \overline{)6},10, 15, 30 \\ \mathrm{GCF}\left(18, 30\right)=6 \end{gathered}$$

5. Find the GCF of 64 and 24

$$\begin{gathered} 64: 1, 2, 4, \overline{)8}, 16, 32, 64 \\ 24: 1, 2, 3, 4, 6,\overline{) 8}, 12, 24 \\ \mathrm{GCF}\left(64, 24\right)=8 \end{gathered}$$

6. Find the LCM of 26 and 39

$$\begin{gathered} 26: 26, 52, \overline{)78}, ... \\ 39: 39, \overline{)78}, ... \\ \mathrm{LCM}\left(26, 39\right)=78 \end{gathered}$$

7. Find the LCM of 60 and 50

$$\begin{gathered} 60: 60, 120, 180, 240, \overline{)300}, ... \\ 50: 50, 100, 150, 200, 250, \overline{)300}, ... \\ \mathrm{LCM}\left(60, 50\right)=300 \end{gathered}$$

8. Find the GCF of 65 and 52

$$\begin{gathered} 65: 1, 5, \overline{)13}, 65 \\ 52: 1, 2, 4, \overline{)13}, 26, 52 \\ \mathrm{GCF}\left(65, 52\right)=13 \end{gathered}$$

9. $\frac{10}{3}·\frac{8}{15}$

$$\begin{gathered} \mathrm{GCF}\left(10, 15\right)=5 \\ \frac{{}^2\cancel{10}}{3}·\frac{8}{{\cancel{15}}_3}=\frac{16}{9} \end{gathered}$$

10. $\frac{18}{25}·\frac{7}{30}$

$$\begin{gathered} \mathrm{GCF}\left(30, 18\right)=6 \\ \frac{7}{{}_5\cancel{30}}·\frac{{\cancel{18}}^3}{25}=\frac{21}{125} \end{gathered}$$

11. $\frac{4}{5}·\frac{5}{6}$

$$\begin{gathered} \mathrm{GCF}\left(4, 6\right)=2; \mathrm{GCF}\left(5, 5\right)=5 \\ \frac{{}^2\cancel{4}}{{}_1\cancel{5}}·\frac{{\cancel{5}}^1}{{\cancel{6}}_3}=\frac{2}{3} \end{gathered}$$

12. $\frac{7}{60}·\frac{50}{21}$

$$\begin{gathered} \mathrm{GCF}\left(7, 21\right)=7; \mathrm{GCF}\left(60, 50\right)=10 \\ \frac{{}^1\cancel{7}}{{}_6\cancel{60}}·\frac{{\cancel{50}}^5}{{\cancel{21}}_3}=\frac{5}{18} \end{gathered}$$

13. $\frac{1}{3}+\frac{1}{15}$

$$\begin{gathered} \mathrm{LCD}\left(3, 15\right)=15 \\ \frac{1}{3}\left(\frac{5}{5}\right)+\frac{1}{15}=\frac{5}{15}+\frac{1}{15} \end{gathered}$$

14. $\frac{9}{8}+\frac{1}{2}$

$$\begin{gathered} \mathrm{LCD}\left(8, 2\right)=8 \\ \frac{9}{8}+\frac{1}{2}\left(\frac{4}{4}\right)=\frac{9}{8}+\frac{4}{8} \end{gathered}$$

15. $\frac{5}{6}+\frac{3}{4}$

$$\begin{gathered} \mathrm{LCD}\left(6, 4\right)=12 \\ \frac{5}{6}\left(\frac{2}{2}\right)+\frac{3}{4}\left(\frac{3}{3}\right)=\frac{10}{12}+\frac{9}{12} \end{gathered}$$

16. $\frac{7}{24}+\frac{5}{18}$

$$\begin{gathered} \mathrm{LCD}\left(24, 18\right)=72 \\ \frac{7}{24}\left(\frac{3}{3}\right)+\frac{5}{18}\left(\frac{4}{4}\right)=\frac{21}{72}+\frac{20}{72} \end{gathered}$$