Multiple smaller nearest

Write the nearest smaller multiple:
number 7 to number 23
number 5 to number 19
number 6 to number 23
number 10 to number 79
number 6 to number 41
number 3 to number 28

Final Answer:

a =  21
b =  15
c =  18
d =  70
e =  36
f =  27

Step-by-step explanation:

$$\begin{gathered} x_1=23/7=\frac{23}{7}=3\frac{2}{7}\doteq 3.2857 \\ a=7\cdot \lfloor x_1\rfloor =7\cdot \lfloor 3.2857\rfloor =21 \end{gathered}$$

$$\begin{gathered} x_2=19/5=\frac{19}{5}=3\frac{4}{5}=3.8 \\ b=5\cdot \lfloor x_2\rfloor =5\cdot \lfloor 3.8\rfloor =15 \end{gathered}$$

$$\begin{gathered} x_3=23/6=\frac{23}{6}=3\frac{5}{6}\doteq 3.8333 \\ c=6\cdot \lfloor x_3\rfloor =6\cdot \lfloor 3.8333\rfloor =18 \end{gathered}$$

$$\begin{gathered} x_4=79/10=\frac{79}{10}=7\frac{9}{10}=7.9 \\ d=10\cdot \lfloor x_4\rfloor =10\cdot \lfloor 7.9\rfloor =70 \end{gathered}$$

$$\begin{gathered} x_5=41/6=\frac{41}{6}=6\frac{5}{6}\doteq 6.8333 \\ e=6\cdot \lfloor x_5\rfloor =6\cdot \lfloor 6.8333\rfloor =36 \end{gathered}$$

$$\begin{gathered} x_6=28/3=\frac{28}{3}=9\frac{1}{3}\doteq 9.3333 \\ f=3\cdot \lfloor x_6\rfloor =3\cdot \lfloor 9.3333\rfloor =27 \end{gathered}$$

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