Step 1

a. The first 10 multiples of 8 are as follows.

\(\displaystyle{8}\times{1}={8}\)

\(\displaystyle{8}\times{2}={16}\)

\(\displaystyle{8}\times{3}={24}\)

\(\displaystyle{8}\times{4}={32}\)

\(\displaystyle{8}\times{5}={40}\)

\(\displaystyle{8}\times{6}={48}\)

\(\displaystyle{8}\times{7}={56}\)

\(\displaystyle{8}\times{8}={64}\)

\(\displaystyle{8}\times{9}={72}\)

\(\displaystyle{8}\times{10}={80}\)

The first 10 multiples of 8 are \(\displaystyle{8},{16},{24},{32},{40},{48},{56},{64},{72},{80}\).

Step 2

b. The first 10 multiples of 12 are as follows.

\(\displaystyle{12}\times{1}={12}\)

\(\displaystyle{12}\times{2}={24}\)

\(\displaystyle{12}\times{3}={36}\)

\(\displaystyle{12}\times{4}={48}\)

\(\displaystyle{12}\times{5}={60}\)

\(\displaystyle{12}{t}{i}{m}{e}{6}={72}\)

\(\displaystyle{12}\times{7}={84}\)

\(\displaystyle{12}\times{8}={96}\)

\(\displaystyle{12}\times{9}={108}\)

\(\displaystyle{12}\times{10}={120}\)

The first 10 multiples of 12 are \(\displaystyle{12},{24},{36},{48},{60},{72},{84},{96},{108},{120}.\)

c. From the lists in part a and b, the common multiples of 8 and 12 in the list are \(\displaystyle{24},{48},{72}.\)

d. From part c, the smallest multiple that 8 and 12 have in common is 24.

a. The first 10 multiples of 8 are as follows.

\(\displaystyle{8}\times{1}={8}\)

\(\displaystyle{8}\times{2}={16}\)

\(\displaystyle{8}\times{3}={24}\)

\(\displaystyle{8}\times{4}={32}\)

\(\displaystyle{8}\times{5}={40}\)

\(\displaystyle{8}\times{6}={48}\)

\(\displaystyle{8}\times{7}={56}\)

\(\displaystyle{8}\times{8}={64}\)

\(\displaystyle{8}\times{9}={72}\)

\(\displaystyle{8}\times{10}={80}\)

The first 10 multiples of 8 are \(\displaystyle{8},{16},{24},{32},{40},{48},{56},{64},{72},{80}\).

Step 2

b. The first 10 multiples of 12 are as follows.

\(\displaystyle{12}\times{1}={12}\)

\(\displaystyle{12}\times{2}={24}\)

\(\displaystyle{12}\times{3}={36}\)

\(\displaystyle{12}\times{4}={48}\)

\(\displaystyle{12}\times{5}={60}\)

\(\displaystyle{12}{t}{i}{m}{e}{6}={72}\)

\(\displaystyle{12}\times{7}={84}\)

\(\displaystyle{12}\times{8}={96}\)

\(\displaystyle{12}\times{9}={108}\)

\(\displaystyle{12}\times{10}={120}\)

The first 10 multiples of 12 are \(\displaystyle{12},{24},{36},{48},{60},{72},{84},{96},{108},{120}.\)

c. From the lists in part a and b, the common multiples of 8 and 12 in the list are \(\displaystyle{24},{48},{72}.\)

d. From part c, the smallest multiple that 8 and 12 have in common is 24.