# What is the common and least multiples of 3 and 6?i want to know how to answer the question!

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In arithmetic the least common multiple (LCM) of two numbers a and b is the smallest positive integer that is a multiple of both a and b.

So, the multiples of 3 are : 3, 6, 9, 12, ...

The multiples of 6 are : 6, 12, ...

So 12 is the first , that is least, common multiple between 3 and 6.

We can solve any lcm problem by doing prime factorization:

To find LCM (3,6).

If n is the LCM(a, b), then n is the least possible number that could be divided by both a and b.

Finding LCM (3,6):

Multiples of 3: 3 , 6, 9, 12,......

Multiple of 6 : 6, 12, 18, 24,............

We see that set {6, 12, 18,.....} appears in both sets of multiple.

So any number in the set {6, 12, 18, 24,.........} is a common multiple of 3 and 6.

Low find the least number among the common mulples set {6, 12, 18, 24,........}. So obviuosly 6 is the least.

So 6 is the least common multiple of 3 and 6. Or LCM(3,6) = 6.

The common and least multiple is also known as the least common multiple or the LCM.

To find the LCM, take both the numbers and express them as a product of prime numbers. Here we get:

3= 3

6= 3 * 2

Now make a set of prime numbers such that all the prime numbers used in expressing the numbers are there in the set. Here if we take 3 and 2, we have 3 which is used to create 3 and 3 and 2 which are used to create 6.

Multiply all the prime numbers in the set. This is the LCM. Here we multiply 3 and 2 giving 6 as the LCM.

**Therefore the common and least multiple of 3 and 6 is 6.**