Birthday ages

Grandma and her granddaughter Barunka have a birthday on the same day. During six consecutive birthday celebrations, Grandma's age was always divisible by Barunka's age. How many birthdays did Grandma celebrate at the last of these six celebrations? Grandma is not more than 100 years old.

Final Answer:

b =  66

Step-by-step explanation:

$$\begin{gathered} 1...\text{ prime number} \\ 2...\text{ prime number} \\ 3...\text{ prime number} \\ 4=2^2 \\ 5...\text{ prime number} \\ 6=2\cdot 3 \\ LCM(1,2,3,4,5,6)=2^2\cdot 3\cdot 5=60 \\ x=LCM(1,2,3,4,5,6)=60 \\ b=x+6=60+6=66 \\ v=6 \\ \text{ Verifying Solution: } \\ {n}_1=b/v=66/6=11 \\ {n}_2=(b-1)/(v-1)=(66-1)/(6-1)=13 \\ {n}_3=(b-2)/(v-2)=(66-2)/(6-2)=16 \\ {n}_4=(b-3)/(v-3)=(66-3)/(6-3)=21 \\ {n}_5=(b-4)/(v-4)=(66-4)/(6-4)=31 \\ {n}_6=(b-5)/(v-5)=(66-5)/(6-5)=61 \end{gathered}$$

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