The LCM, or Least Common Multiple, is just what it sounds like. It’s the smallest number that two or more numbers are a factor of.
One way to find the LCM is to break down the numbers into their prime factors. Once that’s done, you then cancel out the prime factors that are in the smaller number that are also present in the larger number. For example, 6 and 8. If we break down 6, we have 2 × 3, and if we break down 8, we have 2 × 2 × 2. If we look, we can see that 6 has one 2, and 8 has three of them. So we can cancel out that two from our LCM. But 8 doesn’t have a 3, something that 6 has.
So we need to multiply all of the factors of 8, by 3, and we get 24. Let’s do another one. 24 and 14. We break both numbers down: 24 = 2 × 2 × 2 × 3 and 14 = 2 × 7. The number 2 is present in 24 and 14, and 24 has more 2s, meaning that so far, our LCM includes three 2’s. But 24 has no 7, but 14 does, meaning that our LCM has no three 2’s and one 7, or 56.
This can also be applied to polynomials. Once you’ve factored the polynomials completely, you look to see if they have any factors in common. If so, which one has most? That’s the amount you put in the LCM. The rest of the factors that neither polynomial has are then multiplied together with the one that they do have in common, like this:
x2 – 2x – 15 = (x – 5)(x + 3) =>
(x – 5)(x + 3)(x + 1)
x2 – 4x – 5 = (x – 5)(x + 1) =>
Hopefully, you’re starting to get it by now.
The Blogger 
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