Neither 4182

Hanka gave Simon a riddle: guess a pair of numbers whose GCD is 7, and LCM is 90. Katy wanted Šimon to guess such a pair for which GCD is 7, and LCM is 91. Which riddle could Šimon guess?
A: Katy
B: Hankina ​
​C: neither
D: Both

Correct answer:

a =  7
b =  91

Step-by-step explanation:

$$\begin{gathered} 7=1\cdot 7 \\ 90=2\cdot 3\cdot 3\cdot 5 \\ 91=7\cdot 13 \\ a=7 \end{gathered}$$

$$\begin{gathered} b=91 \\ 7...\text{ prime number} \\ 91=7\cdot 13 \\ LCM(7,91)=7\cdot 13=91 \\ x=LCM(7,91)=91 \\ 7...\text{ prime number} \\ 91=7\cdot 13 \\ \text{GCD}(7,91)=7 \\ y=GCD(7,91)=7 \\ b=91 \end{gathered}$$

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