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06 October 06:18   To acquisition the Everyman Accepted Assorted (LCM) of several numbers, we first accurate anniversary amount as a artefact of its prime factors.

For example, if we ambition to acquisition the LCM of 60, 12 and 102 we write



egin

60=2^2 cdot 3 cdot 5 12=2^2 cdot 3 102=2 cdot 3 cdot 17

end

The artefact of the accomplished ability of anniversary altered agency appearing

is the LCM.

For archetype in this case, $2^2cdot3cdot5cdot17=1020$. You can see that 1020 is a assorted of 12, 60 and 102 ... the everyman accepted assorted of all three numbers.

Another example: What is the LCM of 36, 45, and 27?

Solution: Factorise anniversary of the numbers



egin

36=2^2cdot3^245=5cdot3^2 27=3^3

end

The artefact of the accomplished ability of anniversary altered agency appearing

is the LCM, i.e;

$2^2cdot5cdot3^3=540$

If the LCM of the numbers is begin and 1 is subtracted from the LCM then the butt if disconnected by anniversary of the numbers whose LCM is begin would accept a butt that is 1 beneath than the divisor.

For archetype if the LCM of 2 numbers 10 and 9 is 90.

Then 90-1=89 and

89 disconnected by 10 leaves a butt of 9 and the aforementioned amount disconnected by 9 leaves a butt of 8.

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