Dance group

The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?

Result

n =  61

Solution:

$4=2^2 \ \\ 5 \ ... \ prime number \ \\ 6=2 \cdot 3 \ \\ LCM(4, 5, 6)=2^2 \cdot 3 \cdot 5=60 \ \\ \ \\ n=LCM(4,5,6)+1=61$

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