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

kjcdb8er | Certified Educator

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:

neela | Student

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.

william1941 | Student

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.