You know what I mean, right? The number that makes your head spin like a top when you try to calculate it by hand? First things first: LCM stands for “least common multiple.” It’s the smallest number that two or more numbers have in common.
For example, let’s say you want to find the LCM of 12 and 18. You might think it would be easy to just multiply them together (36), but hold your horses! That’s not necessarily true. Why? Because there could be a smaller number that both 12 and 18 divide into evenly.
And guess what, my friends? There is! The LCM of 12 and 18 is actually 36…but wait for it…the smallest common multiple between these two numbers is actually 36 as well! Now you might be thinking: “But why do we care about the least common multiple?” Well, my dear math enthusiasts, there are many reasons.
For one thing, LCMs come up all the time in real-life situations (like figuring out how often to water your plants or how long it takes for a train to make two stops). But more importantly, finding the least common multiple can help us solve other math problems as well. For example, let’s say you want to find the GCD (greatest common divisor) of 12 and 18. To do this, we first need to find their LCM.
Once we have that, we can use a handy-dandy formula:
LCM * GCD = Product of Two Numbers
So if the product of our two numbers is 36 (which it should be), and we know that the least common multiple is also 36 … well, you do the math! The greatest common divisor must be 12.
Now, I’m not going to lie: finding LCMs can still be a bit tricky sometimes. But don’t worry, because there are some handy tricks and shortcuts that can make your life easier (and maybe even save you from pulling out your hair in frustration). For example, did you know that if one of the numbers is a multiple of another number, then their LCM is simply the larger number? For instance, let’s say we want to find the least common multiple between 12 and 36.
Well, since 36 is a multiple of 12 (and also happens to be greater than it), we can skip all that ***** math and just write down “LCM = 36. ”
Another trick you might want to try involves finding the prime factorization of each number. This means breaking them down into their smallest possible factors, which are usually primes (like 2, 3, or 5). Once you have these factors, you can compare them and see if they overlap at all.
If so, then those overlapping factors will be part of the LCM as well! For example, let’s say we want to find the least common multiple between 12 and 36 again (because why not?). The prime factorization for 12 is:
12 = 2 * 2 * 3
And for 36:
36 = 2 * 2 * 2 * 3
As you can see, the factors of 2 and 3 overlap. This means that our LCM will also have those overlapping factors! So we can write down “LCM = 2 * 2 * 2 * 3.” We’ve found it without breaking a sweat (or at least not too much).
It may seem like a math nightmare at first glance, but with a little bit of practice and some handy tricks up your sleeve, you can solve even the most challenging LCM problems in no time!