# What is the LCM of 6 and 4?

Jan 19, 2017

The least common multiple of 6 and 4 is 12.

#### Explanation:

The least common multiple (LCM) is the lowest (least) postive number that two or more numbers can be divided into without a remainder. To find it, you can list the multiples, in order, of the given numbers. For 6, you would list {6, 12 , 18, 24...}. For 4, you would list {4, 8, 12 , 16, 20, 24...}. Then you look for the lowest positive number that these two sets share. In this case, it is 12. As you can see, 12 is the first number which appears in each set. The number 24 is also shared, but it is not the first common multiple, so the answer is 12.

Another method for finding an LCM is by prime factorization, which is breaking down a number into its prime (meaning a number only divisible by itself and 1) factors (meaning the numbers which you multiply in order to get a certain product).

The number 6 breaks down into 3 and 2 (3x2=6), which cannot be divided any further. Four (4) breaks down into 2 and 2 (2x2=4).

Then, multiply the factors by the most amount of times they appear in either set of factors. 2 appears only once in 6's factors, but twice in 4's factors; therefore we multiply 2 by 2 since twice is more than once. The only other different number in these sets is 3, which appears once in 6's factors, so we multiply 3 by 1 . Then we multiply all the chosen numbers together. 2x2x3x1 is 12, so the LCM of 6 and 4 is 12.