  # Least Common Multiple with Numbers

The least common multiple is the smallest number that two or more numbers will divide into evenly. This means that the LCM must contain all the prime factors of each number in question. Suppose we wanted to find the LCM of the numbers 15 and 12. 15's prime factorization is 3 times 5, whereas 12's prime factorization is 2 times 2 times 3. So to find the LCM, we will simply move from left to right putting the missing primes directly into the LCM. Looking at this number 15 here, notice that we have the 3 and the 5 being the primes of 15 so we simply place those into the LCM. Now that we are done with the 15 and we have both the 3 and the 5 in there, we now move to the 12. So notice, in this 12 we've got this 2 times 2 times 3. Notice in the LCM here, the 3 is already there so we can discard the 3. What's missing in this LCM here are these 2's, so we simply place the 2's in the LCM. Now that we are done with both numbers, all we have to do is multiply them all together which, now, that equals 60. But remember the LCM is the smallest number that two or more numbers will divide into evenly. To check ourselves, all we have to do is say 60 divided by 15 equals 4 and 60 divided by 12 equals 5. Both numbers divide evenly, therefore, the definition of LCM is satisfied.

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