For example two numbers 125 and 150 have prime factors 5^3 and 2x3x5^2. Why is the LCM 2x3x5^3? Why does it work?
In: Mathematics
Dumb analogy time. You run a bed-and-breakfast, and you have two guests staying this weekend.
The first guest asks for three different kinds of juice. (juice)^(3), if you will.
The second asks for bagels, eggs, and two different kinds of juice. (bagels)x(eggs)x(juice)^(2), if you will.
You have to make a breakfast that will satisfy both of them; what do you make?
The second one wanted bagels, so you have to include bagels. The second one wanted eggs, so you have to include eggs. They both wanted juice – one wanted two kinds, the other wanted three kinds, so if you serve three kinds they’ll both be happy. Your simplest ‘common’ (works for everybody) breakfast is (bagels)x(eggs)x(juice)^3.
That’s what a lowest common multiple is – it’s the simplest number you can come up with that ‘covers’ all the same components as two or more other numbers.
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