LCM of 3 numbers

[peterliang]

Is the formula for the LCM of 3 numbers x,y,z

t = gcf ( x-y, y-z )

LCM = xyz / 2t

[thething2]

I don't think that works. I tried it and didn't get a right answer.

Usually one number is a factor of another number, so you can eliminate the smaller one and get the LCM of the other 2 numbers. I haven't seen one that you can't do that with yet, so I don't think you need a formula.

[Zac without an H]

Yeah, the first thing I would do is check to see if one of the numbers is a factor of the others, because that would allow you to eliminate the smaller factor and focus on the other two numbers.

If, however, that's not the case, I think you'll have to work it out in a two-step process, though if anyone thinks otherwise feel free to prove me wrong. First, find the LCM of two of the three numbers, then find the LCM of that number and the third number.

Example: Find the LCM of 6, 8, and 9.

The LCM of 6 and 8 is 24.

Now find the LCM of 24 and the remaining number.

The LCM of 24 and 9 is 72.

The LCM of 6, 8, and 9 is 72.

[AuSmith]

Peter, the 2 in your conjecture should stand out to you. When dealing with prime factorizations, 2 is in nearly every way the same as any other prime 3,5,7,... so it would seem just as plausible to me to use 8191 instead of 2. What if x,y,z were all odd? I'm going with Zac (like the name). At first LCM, like a lot of things, is defined as a binary operation (plus, times, intersection, union, etc). But, since it's associative, i.e.

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then we can "get rid of parenthesis" and formulate a well-defined LCM of three or four numbers - just take two at a time.

Though if you want a more algebraically pleasing formula for LCM, I think you might use the inclusion-exclusion principle.

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[bradp]

if you are asking this as it relates to NS, the questions sometimes have one of the numbers as a multiple of the other like others have said.

like find the LCM of 12,72, and 44... LCM of 12 and 72 is 72... lcm of 72 and 44 is

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