Two rulers

We have two rulers. The scale interval on the first ruler is spaced 1 cm, and on the second is 15 mm. Rulers are attached to match the initial divider commas. What next dividers commas coincide? Find at least three cases.

Correct answer:

a =  30 mm
b =  60 mm
c =  90 mm
d =  210 mm

Step-by-step explanation:

$$\begin{gathered} x=1\text{cm}\to \text{mm}=1\cdot 10\text{mm}=10\text{mm} \\ y=15\text{mm} \\ 10=2\cdot 5 \\ 15=3\cdot 5 \\ LCM(10,15)=2\cdot 3\cdot 5=30 \\ w=LCM(x,y)=LCM(10,15)=30 \\ a=1\cdot w=1\cdot 30=30\text{mm} \end{gathered}$$

$b=2\cdot w=2\cdot 30=60\text{mm}$

$c=3\cdot w=3\cdot 30=90\text{mm}$

$d=7\cdot w=7\cdot 30=210\text{mm}$

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