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

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

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 | High School Teacher | (Level 3) Valedictorian

Posted on

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 | College Teacher | (Level 3) Valedictorian

Posted on

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.