When you add two numbers in Lego you keep the colours that are shared and drop the colours that are not shared. This works because when you add two multiples of any number, you get another multiple of that number.
$an+bn=(a+b)n$
Adding two even numbers gives another even number. These are the multiples of 2: all the numbers which contain a blue block.
Numbers are relatively prime if they don't share any prime factors. In Lego this means that numbers are relatively prime if they don't share any colours.
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