LCM of 3, 4, and 5 is the the smallest number among all common multiples that 3, 4, and 5. The first few multiples that 3, 4, and 5 space (3, 6, 9, 12, 15 . . .), (4, 8, 12, 16, 20 . . .), and also (5, 10, 15, 20, 25 . . .) respectively. There space 3 commonly used approaches to uncover LCM of 3, 4, 5 - by listing multiples, by division method, and also by prime factorization.

You are watching: Least common multiple of 3 4 and 5

1.LCM the 3, 4, and also 5
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM the 3, 4, and 5 is 60.

*

Explanation:

The LCM of 3 non-zero integers, a(3), b(4), and also c(5), is the smallest hopeful integer m(60) that is divisible by a(3), b(4), and c(5) without any kind of remainder.


Let's look in ~ the various methods because that finding the LCM that 3, 4, and 5.

By element Factorization MethodBy division MethodBy Listing Multiples

LCM of 3, 4, and also 5 by prime Factorization

Prime factorization of 3, 4, and 5 is (3) = 31, (2 × 2) = 22, and (5) = 51 respectively. LCM of 3, 4, and 5 have the right to be derived by multiply prime determinants raised to their respective greatest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM of 3, 4, and 5 by prime factorization is 60.

LCM of 3, 4, and 5 by division Method

*

To calculation the LCM the 3, 4, and 5 through the department method, we will divide the numbers(3, 4, 5) by your prime determinants (preferably common). The product of this divisors gives the LCM the 3, 4, and 5.

Step 2: If any type of of the offered numbers (3, 4, 5) is a lot of of 2, division it through 2 and write the quotient listed below it. Carry down any kind of number the is not divisible by the element number.Step 3: continue the procedures until just 1s are left in the critical row.

The LCM that 3, 4, and also 5 is the product of every prime numbers on the left, i.e. LCM(3, 4, 5) by department method = 2 × 2 × 3 × 5 = 60.

LCM that 3, 4, and also 5 by Listing Multiples

*

To calculate the LCM of 3, 4, 5 by listing out the common multiples, we deserve to follow the given listed below steps:

Step 1: list a couple of multiples that 3 (3, 6, 9, 12, 15 . . .), 4 (4, 8, 12, 16, 20 . . .), and also 5 (5, 10, 15, 20, 25 . . .).Step 2: The usual multiples indigenous the multiples of 3, 4, and also 5 space 60, 120, . . .Step 3: The smallest typical multiple that 3, 4, and 5 is 60.

∴ The least typical multiple that 3, 4, and 5 = 60.

☛ additionally Check:


Example 2: find the smallest number the is divisible through 3, 4, 5 exactly.

Solution:

The worth of LCM(3, 4, 5) will be the the smallest number the is precisely divisible by 3, 4, and 5.⇒ Multiples that 3, 4, and also 5:

Multiples the 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 52, 56, 60, . . . .Multiples that 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .

Therefore, the LCM the 3, 4, and 5 is 60.


Example 3: Verify the relationship in between the GCD and also LCM of 3, 4, and also 5.

Solution:

The relation between GCD and LCM the 3, 4, and 5 is offered as,LCM(3, 4, 5) = <(3 × 4 × 5) × GCD(3, 4, 5)>/⇒ element factorization the 3, 4 and also 5:

3 = 314 = 225 = 51

∴ GCD of (3, 4), (4, 5), (3, 5) and also (3, 4, 5) = 1, 1, 1 and also 1 respectively.Now, LHS = LCM(3, 4, 5) = 60.And, RHS = <(3 × 4 × 5) × GCD(3, 4, 5)>/ = <(60) × 1>/<1 × 1 × 1> = 60LHS = RHS = 60.Hence verified.


Show systems >

go to slidego to slidego come slide


*


FAQs ~ above LCM the 3, 4, and also 5

What is the LCM that 3, 4, and 5?

The LCM of 3, 4, and also 5 is 60. To find the least usual multiple the 3, 4, and 5, we need to find the multiples that 3, 4, and also 5 (multiples the 3 = 3, 6, 9, 12 . . . . 60 . . . . ; multiples the 4 = 4, 8, 12, 16 . . . . 60 . . . . ; multiples the 5 = 5, 10, 15, 20 . . . . 60 . . . . ) and also choose the smallest multiple that is specifically divisible by 3, 4, and also 5, i.e., 60.

What is the Relation in between GCF and also LCM the 3, 4, 5?

The complying with equation deserve to be used to express the relation in between GCF and LCM of 3, 4, 5, i.e. LCM(3, 4, 5) = <(3 × 4 × 5) × GCF(3, 4, 5)>/.

How to find the LCM of 3, 4, and 5 by prime Factorization?

To uncover the LCM of 3, 4, and also 5 making use of prime factorization, us will uncover the prime factors, (3 = 31), (4 = 22), and (5 = 51). LCM the 3, 4, and 5 is the product that prime determinants raised to your respective highest exponent amongst the number 3, 4, and also 5.⇒ LCM of 3, 4, 5 = 22 × 31 × 51 = 60.

See more: How Many Nanoseconds In A Century Conversion Calculator, Centuries To Nanoseconds Conversion

Which the the adhering to is the LCM of 3, 4, and also 5? 28, 20, 5, 60

The value of LCM of 3, 4, 5 is the smallest common multiple that 3, 4, and also 5. The number to solve the given problem is 60.