
Least common multiple (LCM)
The least common multiple, or LCM, of two or more numbers is the least of their common multiples, excluding zero.
There are different ways to find the LCM of numbers. Look at them and choose the one you prefer!!!
List the nonzero multiples
List the multiples of the larger number and stop when you find a multiple of the other number. This is the LCM.
Find the LCM of 6 and 8.
List the multiples of 6 until you come to a number that is also a multiple of 8.
The multiples of 6 are 6, 12, 18, 24, ...
The multiples of 8 are 8, 16, 24, ...
So, LCM(6,8) = 24.
Use prime factorization
To find the LCM of a set of numbers, you must factor each of the numbers into primes. Then for each different prime number in all of the factorizations, do the following...
1. Count the number of times each prime number appears in each of the factorizations.
2. For each prime number, take the largest of these counts and write the result.
3. The least common multiple is the product of all the prime numbers written down.
Example: LCM (4,6)=12, because 4=2·2 and 6=2·3, so LCM(4,6)=2·2·3
Find LCM(16,24,40)
1. Determine the prime factorization of each number:
16=2^{4}
24=2^{3}·3
40=2^{3}·5
2. Take the prime numbers that appears in all the factorizations. (Remember taking the highest number of times they appear). Prime numbers selected: 2, 3, and 5
3. LCM(16,24,40) = 2 ^{4}·3·5 = 240
