Can someone tell me about this?
2006-09-17 10:39:45 · 6 answers · asked by Happily in love 1 in Science & Mathematics ➔ Mathematics
ok...how is the least common multible found?
2006-09-17 10:48:58 · update #1
Hi there. Here is the best way I know of to find the least common multiple (it's also the fastest). It'll require that you search for the Euclidean Algorithm online, which I'll explain in a minute.
It's a fact (proven usually in one's second semester of abstract algebra or first semester of undergraduate number theory, so don't worry about the proof) that given two numbers m,n, the least common multiple is given by:
lcm(m,n)=((m)(n))/(gcd(m,n)).
In words, the least common multiple is found by multiplying the two numbers together and then dividing by their greatest common divisor. This means that finding the least common multiple is just as fast as finding the greatest common divisor! This is where the Euclidean Algorithm comes in.
The Euclidean Algorithm is a very fast method of finding the least common multiple of two numbers. I've attached a link for you to look it up. I *highly* recommend you teach it to yourself, as it will literally save hours off your life (and it's not that difficult). That's all there is to it because once you have the gcd you have the lcm for free.
Let's do an example. Suppose I wanted the least common multiple of 280 and 720. Start by finding their gcd:
720= 2(280)+160
280= 1(160)+120
160= 1(120)+40
120= 3(40)
So using the Euclidean Algorithm (see how fast that was? four steps for numbers that big), we get the gcd(280,720)=40. Now we simply take (280)(720)=201600 and divide this by 40 to get that lcm(280,720)=5040.
Hope this helps!!!
2006-09-17 11:39:14 · answer #1 · answered by wlfgngpck 4 · 0⤊ 0⤋
The least common multiple of two numbers is easy to find once you get the hang of it. All you have to do is find the smallest number that the two numbers will both go into. Some examples are:
2 and 4 would be 4 because 2 can go into four and you would get 2 and 4 would go into 4 and you would get 1. Also:
4 and 6 would be 24 because 24/4=6 and 24/6=4
4 and 8 would be 8 because 8/4=2 and 8/8=1
Good Luck in math :)
2006-09-17 10:49:38 · answer #2 · answered by american_girl_24_7 1 · 0⤊ 0⤋
Multiples are products of numbers. Example: multiples of 3 are 6, 9, 12, 15, 18, 21, 24..... Multiples of 4 are 8, 12, 16, 20, 24, 28.... Notice that 12 and 24 are both multiples of 3 and 4. Since 12 is the smallest, it's called the 'least common multiple.'
To compute, break each number into factors:
Example: Find the least common multiple of 18 and 15.
18 = 2 x 3 x 3
15 = 3 x 5
Now, use the 'most' of each factor: 2 x 3 x 3 x 5 = 90
2006-09-17 10:46:38 · answer #3 · answered by tlf 3 · 0⤊ 0⤋
The Least Common Multiple (LCM) of two or more numbers is the smallest number that all the numbers in question will divide into. For instance, the LCM of 6 and 8 is 24.
2006-09-17 10:42:50 · answer #4 · answered by Chris S 5 · 0⤊ 0⤋
In arithmetic and number theory the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b. If there is no such positive integer, e.g., if a = 0 or b = 0, then lcm(a, b) is defined to be zero.
When adding or subtracting vulgar fractions, it is useful to find the least common multiple of the denominators, often called the lowest common denominator.
2006-09-17 10:46:24 · answer #5 · answered by math geek 3 · 0⤊ 0⤋
Well the LCM of numbers is the smallest number that has all of the aforementioned numbers as factors.
2006-09-17 10:44:45 · answer #6 · answered by dennismeng90 6 · 0⤊ 0⤋