LCM that 3, 4, and 5 is the the smallest number amongst all typical multiples of 3, 4, and also 5. The first couple of 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 room 3 commonly used methods to uncover LCM the 3, 4, 5 - by listing multiples, by department method, and by prime factorization.

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

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

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Explanation:

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


Let's look at the different methods for finding the LCM the 3, 4, and also 5.

By element Factorization MethodBy department MethodBy Listing Multiples

LCM that 3, 4, and 5 by prime Factorization

Prime factorization of 3, 4, and 5 is (3) = 31, (2 × 2) = 22, and (5) = 51 respectively. LCM the 3, 4, and also 5 can be acquired by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM that 3, 4, and also 5 by prime factorization is 60.

LCM the 3, 4, and also 5 by division Method

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To calculation the LCM the 3, 4, and also 5 through the division 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 kind of of the provided numbers (3, 4, 5) is a lot of of 2, divide it by 2 and write the quotient below it. Bring down any type of number that is not divisible by the prime number.Step 3: proceed the procedures until just 1s space left in the critical row.

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

LCM of 3, 4, and 5 by Listing Multiples

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To calculation the LCM that 3, 4, 5 through listing out the usual multiples, we have the right to follow the given below steps:

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

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

☛ also Check:


Example 2: uncover the the smallest number the is divisible by 3, 4, 5 exactly.

Solution:

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

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

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


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

Solution:

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

3 = 314 = 225 = 51

∴ GCD that (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.


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FAQs top top LCM of 3, 4, and 5

What is the LCM of 3, 4, and also 5?

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

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

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

How to uncover the LCM the 3, 4, and also 5 by element Factorization?

To find the LCM that 3, 4, and also 5 making use of prime factorization, we will discover the element factors, (3 = 31), (4 = 22), and also (5 = 51). LCM the 3, 4, and 5 is the product the prime determinants raised to their respective highest exponent among the number 3, 4, and also 5.⇒ LCM that 3, 4, 5 = 22 × 31 × 51 = 60.

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

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