What is the maximum order of any element in AzoSolutionHere

What is the maximum order of any element in Azo

Solution

Here is A₂₀.

So, First break 20 into different sums.

20 = 1+2+3+4+10

LCM (1,2,3,4,10) = 60

20 = 1+2+3+5+9

LCM (1,2,3,5,9) = 90

20 = 1+2+3+6+8

LCM (1,2,3,6,8) = 24

20 = 1+2+3+7+7

LCM (1,2,3,7,7) = 42

20 = 1+2+3+14

LCM (1,2,3,14) = 42

20 = 1+2+4+13

LCM (1,2,4,13) = 52

20 = 5+7+8

LCM (5,7,8) = 280

Hence 280 is maximum order.