Glimpses of Puzzles - Part 3

Description of Glimpses of Puzzles - Part 3

ENJOY THIS PUZZLE GAME !!!
This game consists of following three puzzles :
Puzzle Mode1 :
A locker has 16 switches arranged in a 4 by 4 grid.
In order to open it, all the 16 switches must be in the on state.
When a switch is toggled, all the other switches in the same row and column are also toggled.
It is shown that whatever the initial state of the switches, it is always possible to open the locker.
Puzzle Mode2 :
64 numbers 1 to 64 are written on each cell of a 8 by 8 grid.
Cells are numbered from left to right then fron top to bottom and so on i.e
01 02 03 04 ... 08
09 10 11 12 ... 16
...
57 58 59 60 ... 64
With each click of a cell, if the first cell is numbered n then all the cells from 1 to n are reversed.
It is shown that eventually the first cell number will be 1.
Puzzle Mode3 :
16 distinct positive integers are written on each cell of a 4 by 4 grid.
If you select any two numbers then that two numbers will be changed to their gcd (greatest common divisor) and lcm (least common multiple).
First number selected will be highlighted by red boundary.
It is shown that eventually the numbers will stop changing i.e the positions of numbers may change but their values will be constant.
Please check the numbers written on the board and confirm.
Continue playing till you are not convinced.
This game is ABSOLUTELY FREE and contains NO-ADS or IN-APP PURCHASES.
In case of any bug please email me.