LCM the 6, 12, and 15 is the the smallest number among all usual multiples the 6, 12, and 15. The first few multiples of 6, 12, and 15 are (6, 12, 18, 24, 30 . . .), (12, 24, 36, 48, 60 . . .), and (15, 30, 45, 60, 75 . . .) respectively. There are 3 commonly used methods to discover LCM that 6, 12, 15 - through listing multiples, by division method, and by element factorization.

You are watching: Least common multiple of 6 12 and 15

1.LCM that 6, 12, and also 15
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 6, 12, and 15 is 60.

*

Explanation:

The LCM of 3 non-zero integers, a(6), b(12), and also c(15), is the smallest hopeful integer m(60) that is divisible by a(6), b(12), and also c(15) without any kind of remainder.


Let's look at the various methods because that finding the LCM of 6, 12, and also 15.

By department MethodBy prime Factorization MethodBy Listing Multiples

LCM the 6, 12, and 15 by division Method

*

To calculate the LCM of 6, 12, and also 15 by the division method, we will certainly divide the numbers(6, 12, 15) by their prime components (preferably common). The product of these divisors offers the LCM of 6, 12, and also 15.

Step 2: If any of the given numbers (6, 12, 15) is a many of 2, divide it by 2 and write the quotient listed below it. Carry down any number the is not divisible by the element number.Step 3: proceed the procedures until only 1s space left in the last row.

The LCM of 6, 12, and 15 is the product of all prime number on the left, i.e. LCM(6, 12, 15) by division method = 2 × 2 × 3 × 5 = 60.

LCM that 6, 12, and 15 by element Factorization

Prime administer of 6, 12, and 15 is (2 × 3) = 21 × 31, (2 × 2 × 3) = 22 × 31, and also (3 × 5) = 31 × 51 respectively. LCM that 6, 12, and also 15 can be obtained by multiply prime factors raised to their respective greatest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM the 6, 12, and also 15 by prime factorization is 60.

LCM of 6, 12, and also 15 by Listing Multiples

To calculation the LCM that 6, 12, 15 by listing the end the typical multiples, we can follow the given listed below steps:

Step 1: list a couple of multiples that 6 (6, 12, 18, 24, 30 . . .), 12 (12, 24, 36, 48, 60 . . .), and 15 (15, 30, 45, 60, 75 . . .).Step 2: The usual multiples from the multiples that 6, 12, and 15 are 60, 120, . . .Step 3: The smallest typical multiple the 6, 12, and also 15 is 60.

∴ The least typical multiple of 6, 12, and 15 = 60.

☛ also Check:


Example 1: Verify the relationship in between the GCD and also LCM of 6, 12, and 15.

Solution:

The relation in between GCD and also LCM of 6, 12, and also 15 is given as,LCM(6, 12, 15) = <(6 × 12 × 15) × GCD(6, 12, 15)>/⇒ prime factorization of 6, 12 and 15:

6 = 21 × 3112 = 22 × 3115 = 31 × 51

∴ GCD that (6, 12), (12, 15), (6, 15) and also (6, 12, 15) = 6, 3, 3 and 3 respectively.Now, LHS = LCM(6, 12, 15) = 60.And, RHS = <(6 × 12 × 15) × GCD(6, 12, 15)>/ = <(1080) × 3>/<6 × 3 × 3> = 60LHS = RHS = 60.Hence verified.


Example 2: calculate the LCM that 6, 12, and 15 utilizing the GCD that the given numbers.

Solution:

Prime administrate of 6, 12, 15:

6 = 21 × 3112 = 22 × 3115 = 31 × 51

Therefore, GCD(6, 12) = 6, GCD(12, 15) = 3, GCD(6, 15) = 3, GCD(6, 12, 15) = 3We know,LCM(6, 12, 15) = <(6 × 12 × 15) × GCD(6, 12, 15)>/LCM(6, 12, 15) = (1080 × 3)/(6 × 3 × 3) = 60⇒LCM(6, 12, 15) = 60


Example 3: find the smallest number the is divisible by 6, 12, 15 exactly.

Solution:

The smallest number the is divisible through 6, 12, and also 15 specifically is their LCM.⇒ Multiples the 6, 12, and also 15:

Multiples that 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . .Multiples the 12 = 12, 24, 36, 48, 60, 72, . . . .Multiples of 15 = 15, 30, 45, 60, 75, 90, . . . .

Therefore, the LCM the 6, 12, and 15 is 60.


Show equipment >

go to slidego to slidego come slide


*


FAQs top top LCM that 6, 12, and also 15

What is the LCM of 6, 12, and also 15?

The LCM that 6, 12, and 15 is 60. To find the least usual multiple of 6, 12, and 15, we require to uncover the multiples the 6, 12, and 15 (multiples that 6 = 6, 12, 18, 24 . . . . 60 . . . . ; multiples the 12 = 12, 24, 36, 48 . . . . 60 . . . . ; multiples that 15 = 15, 30, 45, 60 . . . .) and also choose the smallest multiple that is precisely divisible by 6, 12, and also 15, i.e., 60.

What is the the very least Perfect Square Divisible through 6, 12, and 15?

The the very least number divisible by 6, 12, and also 15 = LCM(6, 12, 15)LCM of 6, 12, and also 15 = 2 × 2 × 3 × 5 ⇒ the very least perfect square divisible by every 6, 12, and also 15 = LCM(6, 12, 15) × 3 × 5 = 900 Therefore, 900 is the compelled number.

How to discover the LCM that 6, 12, and 15 by element Factorization?

To discover the LCM that 6, 12, and 15 using prime factorization, us will uncover the element factors, (6 = 21 × 31), (12 = 22 × 31), and also (15 = 31 × 51). LCM of 6, 12, and 15 is the product the prime determinants raised to their respective highest exponent amongst the number 6, 12, and also 15.⇒ LCM the 6, 12, 15 = 22 × 31 × 51 = 60.

See more: How Far Is 1000 Meters In Feet, 1000 M To Ft 1000 Meters To Feet

Which of the following is the LCM of 6, 12, and also 15? 18, 60, 28, 11

The worth of LCM that 6, 12, 15 is the smallest usual multiple that 6, 12, and also 15. The number to solve the given problem is 60.