LCM of 3 and also 6 is the the smallest number amongst all common multiples that 3 and 6. The first couple of multiples the 3 and 6 space (3, 6, 9, 12, 15, 18, 21, . . . ) and (6, 12, 18, 24, 30, 36, 42, . . . ) respectively. There space 3 generally used techniques to find LCM of 3 and 6 - by listing multiples, by department method, and by prime factorization.

You are watching: Least common multiple of 6 and 3

1.LCM the 3 and 6
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 3 and also 6 is 6.

*

Explanation:

The LCM of two non-zero integers, x(3) and also y(6), is the smallest optimistic integer m(6) the is divisible by both x(3) and y(6) without any type of remainder.


Let's look at the different methods because that finding the LCM that 3 and also 6.

By element Factorization MethodBy Listing MultiplesBy division Method

LCM the 3 and also 6 by prime Factorization

Prime administer of 3 and 6 is (3) = 31 and also (2 × 3) = 21 × 31 respectively. LCM that 3 and 6 can be acquired by multiplying prime factors raised to their respective greatest power, i.e. 21 × 31 = 6.Hence, the LCM the 3 and 6 by prime factorization is 6.

LCM of 3 and 6 by Listing Multiples

*

To calculate the LCM that 3 and 6 by listing out the typical multiples, we deserve to follow the given below steps:

Step 1: list a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 6 (6, 12, 18, 24, 30, 36, 42, . . . . )Step 2: The typical multiples from the multiples of 3 and also 6 room 6, 12, . . .Step 3: The smallest usual multiple that 3 and 6 is 6.

∴ The least typical multiple that 3 and 6 = 6.

LCM that 3 and 6 by department Method

*

To calculate the LCM that 3 and 6 through the department method, we will certainly divide the numbers(3, 6) by their prime determinants (preferably common). The product of this divisors gives the LCM the 3 and 6.

Step 3: proceed the measures until just 1s are left in the last row.

See more: What Is Cooking An Egg A Chemical Or Physical Change ? What Is The Chemical Reaction When Cooking An Egg

The LCM that 3 and 6 is the product of every prime number on the left, i.e. LCM(3, 6) by department method = 2 × 3 = 6.